LIBRARY OF THE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN coo/2. The person charging this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN ^7^ OCT SEP 15^ L161 — O-1096 Digitized by the Internet Archive in 2013 http://archive.org/details/transformatrixim393marv REPORT NO. 393 3*3 jfrisL^ou C00-1U69-0161 April, I97O TRANS FORMATRIX AN IMAGE PROCESSOR INPUT AND STOCHASTIC PROCESSOR SECTIONS by ORIN EDWARD MARVEL Report No. 393 TRANSFORMATRIX AN IMAGE PROCESSOR INPUT AND STOCHASTIC PROCESSOR SECTIONS* by ORIN EDWARD MARVEL April, 1970 Department of Computer Science University of Illinois Urbana, Illinois 6l801 * Supported in part by Contract Number U. S. AEC AT(ll-l) lk69 and submitted in partial fulfillment for the degree of Doctor of Philosophy in Electrical Engineering, at the university of Illinois, April, 1970. TRANS FORMATRIX - AN IMAGE PROCESSOR, INPUT AND STOCHASTIC PROCESSOR SECTIONS Or in Edward Marvel, Ph.D. Department of Electrical Engineering University of Illinois, 1970 A new scheme of picture processing at television rates is proposed, in which a two dimensional input picture, x. ., is transformed into an output picture, y „ , according to the linear transform: 31 31 y ki = iio jio h ±M ' x ij i, j, k, £ = 0, 1, . . ., 31 This thesis describes the input image processor, stochastic processor, and input display channel. The input image processor applies the asymetrical rise and fall time of a photoconductor to dynamically convert a scanned television image into parallel form. In order to select a suitable photoconductor, a computer model of the television-photoconductor dynamics was derived. The stochastic processor converts the input signals to Synchronous Random Pulse Sequences and performs the 102^ parallel multiplications b. . • x. .. To better understand Random Pulse Sequence multiplication, a study of pseudo-random number generation and an error analysis of Random Pulse Sequence representation was performed. The input display channel mutiplexes the x. .'s in order to display the input image. It, also, allows the operator to select a linear or logarithmic sensation display. This thesis concludes with the derivation of a theorem relating the accuracy of the stochastic processor to the resolution of the picture processed, Ill ACKNOWLEDGMENTS The author wishes to thank Professor W. J. Poppelbaum for his original suggestion for this thesis topic and for his advice, criticism, and many in- valuable suggestions throughout the course of this project. He is also indebted to his partners, L. D. Ryan and Y. Wo, who helped build the Transformatrix system. In addition, he would like to thank Miss Car la Donaldson for the typing, and all the members of the fabrication group under Mr. Frank Serio for their individual contributions. Last, but not least, he would like to thank his wife, JoAnn, for her patient and willing help. IV TABLE OF CONTENTS Page 1. INTRODUCTION 1 2. FUNCTIONS PERFORMED BY TRANSFORMATRIX 3 2.1 Co-ordinate Transform 3 2.2 Pattern Recognition 5 2.3 Two Dimensional Fourier Transform 5 3. SYSTEM DESCRIPTION 8 3.1 Block Diagram 8 3.2 Timing 10 4. STOCHASTIC PROCESSOR 13 4.1 Synchronous Random Pulse Sequence Representation ... 13 4.2 Synchronous Random Pulse Sequence Multiplication . . . 14 4.3 Quantized Random Analog Signal Generation 14 4.3.1 Pseudo Random Bit Generators 16 4.3.2 Coefficient Channel Quantized Random Analog Signal Generation 27 4.3.3 Picture Input Channel Quantized Random Analog Signal Generation 28 4.3.4 Quantized Random Analog Signal Digital to Analog Conversion 30 4.4 Conversion of Voltages to Synchronous Random Pulse Sequences 43 4.5 Stochastic Processor Card 43 4.6 Conversion of a Synchronous Random Pulse Sequence to a Voltage 46 5. INPUT IMAGE PROCESSOR 51 5.1 Review of the Characteristics of a Television Receiver 51 5.2 Conversion of a Scanned Television Image to Parallel Voltages 52 5.2.1 Synchronous Conversion with Digital Storage . . 52 5.2.2 Synchronous Conversion with Analog Storage . . 52 5.2.3 Asynchronous Conversion Using Photoconductors . 52 5.3 Construction of Photoconductors 55 5.4 Physics of Photoconductivity „ 55 5.5 Phot oconduc tor System Characteristics 62 5.5.1 Spectral Response 62 5.5.2 Nonlinear Transfer Function 64 5.5.3 Asymetrical Transient Response 64 5.6 Input Image Processor Card 66 5.6.1 Standardizing the Photoconductor Transfer Function TO 5.6.2 Linearizing the Photoconductor Transfer Function 72 Page 5.7 The Dynamic Response of Photo conductors Illuminated by a Television Receiver 72 5.7.I Response for Simplest Television Receiver Model 73 5.7*2 Response for Regular Television Model 8h 6. INPUT IMAGE DISPLAY CHANNEL 95 6.1 System Operation 95 6.2 Logarithmic Sensation Display 97 6.3 Linear Sensation Display 102 7. A GENERALIZED TRANSFORMATRIX PROCESSOR 10*+ 7.1 Resolution 10^ 7-2 Rule Relating Accuracy, Resolution, and Bandwidth When Processing Television Images . . . <, 10U 8. CONCLUSIONS 110 APPENDIX 112 LIST OF REFERENCES 122 VITA 12l+ VI LIST OF TABLES Table Page 1. Truth Table for a Modulo Two Adder . . . . 19 2. 325 Sequences of a 33 Stage Pseudo Random Bit Generator . 21 3. QRAS Levels for Coefficient and Input Picture Channels . . 4l h. Photoconductor Characteristics . . . . „ 67 Vll LIST OF FIGURES Figure Page 1.1 TRANSFORMATRLX Concept 2 2.1 Translation Example 4 2.2 Pattern Recognition Example 6 3.1 Block Diagram „ 9 3.2 Timing Diagram „ 12 4.1 Synchronous Random Pulse Sequence Multiplication .... 15 4.2 Pseudo Random Bit Concept 17 4.3 5 Stage Pseudo Random Bit Generator 18 4.4 Input Voltage to SRPS Conversion 23 4.5 QRAS Generation 24 4.6 Run Number 3 of Table 2 26 4.7 Coefficient Channel QRAS Generator 29 4.8 6 Stage Pseudo Random Bit Generator 31 4.9 Input Channel QRAS Generator . . . . 32 4.10 Examples of Voltage Spikes Being Produced 34 4.11 First Half of the QRAS "Shorting Switch" Decoder .... 35 4.12 Second Half of the QRAS "Shorting Switch" Decoder ... 36 4.13 First Half of Computer Program that Determines the Values of the Resistive Ladder 38 4.14 Second Half of Computer Program that Determines the Values of the Resistive Ladder 39 4.15 Schematic and Model of the Resistive Ladder Driver ... 40 4.16 Schematic of National NH0002 42 4.17 Stochastic Processor Card 44 .18 Stochastic Processor Cell 45 VI 11 Figure Page k,19 Percentage Error Versus SRPS Value 50 5.1 Synchronous Conversion with Digital Storage 53 5.2 Synchronous Conversion with Analog Storage 5^ 5.3 Phot oconduc tor 56 5.4 Drawing of Simple Photoconductor „ . . . 57 5.5 SRH Centers Capturing and Emitting Electrons 59 5.6 Classification of SRH Centers 6l 5.7 Spectral Response of a T-h Television Phosphor and Selected Photoconductor 63 5.8 Photoconductor ' s Transfer Function 65 5.9 Input Image Processor Card 68 5.10 Input Image Processor Cell 69 5.11 Intensity to SRPS Converter . . . . „ "Jl 5.12 Response of Photoconductor to TV Receiver 7^ 5.13 Program for Response to 32 by 32 TV System 77 5.1^ Program for Response to 32 by 32 TV System 78 5.15 Response A for 32 by 32 TV Model 79 5.16 Response B for 32 by 32 TV Model 80 5.17 Response C for 32 by 32 TV Model 8l 5.18 Response for 16 Microsecond Beam 82 5.19 Response for 6 Microsecond Beam 83 5.20 Program for Difference Equation Response 85 5.21 Program for Difference Equation Response 86 5.22 Response A for Difference Equation Response 87 5.23 Program for Final Model 89 5.24 Program for Final Model 90 IX Figure Page 5.25 Response for Device A 91 5.26 Response for Device B 92 5.27 Response for Device D j3 5.28 Response for Device G -jk 6.1 Block Diagram of Input Image Display Channel j6 6.2 Tektronix 602 Oscilloscope Transfer Function 99 6.3 Program for Logarithmic Display „ . . . . 100 6.h z Axis Drive for the Logarithmic and Linear Displays . . 101 6.5 Program for Linear Display 103 7.1 A Picture with Poor Resolution in the Horizontal Direction 105 7.2 Plot of Accuracy Versus Resolution 109 .1 Picture of "Model T" Ill A.l Fourier Transform Program . 114 A. 2 Fourier Transform Program 115 A. 3 Example 1 of the Fourier Transform 116 A.k Example 2 of the Fourier Transform 117 A. 5 Example 3 of the Fourier Transform 118 A. 6 Example k of the Fourier Transform 119 A. 7 Example 5 of the Fourier Transform 120 A. 8 Example 6 of the Fourier Transform 121 1. INTRODUCTION The purpose of this thesis is to apply the unusual characteristics of stochastic sequences and the non-linear dynamics of photoconductors to the parallel processing of images. Success in this area will enhance mans' ability to use one of his greatest senses, that of sight. The TRANS FORMATRIX machine, as originally conceived by Professor W. J. Poppelbaum, ' ' is an application of stochastic processing in which the light values furnished by a 32 by 32 photoconductor matrix are transformed into 1021+ stochastic sequences. These sequences are multiplied one by one by 1024 coefficients, defined by a coefficient matrix (or more exactly, by their stochastic sequences). The sum of these multiplications is displayed as a 32 by 32 output image on a cathode ray tube. The collection of 1024 different 32 by 32 coefficient matrices defines all possible translations, rotations, magnifications, convolutions, conformal mappings, and two dimensional Fourier Transforms. The generalized concept of the system is shown pictorially in Figure 1.1. This thesis describes the theoretical justification and design of the input image processor, stochastic processor and input display channel of Transf ormatrix . < X 5 LU < uj o u. U. LlJ O o >- CD UJ < u. o UJ C/5 ID UJ UJ H < CL < 2 S CO 3 i I ^o o o o o o ' V o o o o o o / = < O O O ;^» O O o o o * o o -Q / / o o o o o o c o o o o o o V- J c C -Q JQ N ^ X CO < or ■& CD o o o H 3 o CO H 0) •H 2. FUNCTIONS PERFORMED BY TRANS FORMATRIX The coefficient matrices, that are delivered to the stochastic processor, determine which transformation is performed. In order to demonstrate the versatility of Transformatrix, three different image transforms, each with a number of different applications, were implemented. 2.1 Co-ordinate Transform To ease image interpretation, it is often desirable to reorient the given image by translating it in the horizontal and vertical directions; magnifying it; or rotating the picture about the geometric center. Figure 2.1 shows an image being translated one unit to the right. The location of a "1" in any coefficient matrix, Figure 2.1, determines which input pattern's intensity is to be multiplexed to the output point specified by that matrix. Let (u,v) represent the quantized co-ordinates of a point in the input pattern. Under co-ordinate transformation, the intensity at (u,v,) is multiplexed to a point (U,V) in the output pattern given by: U = m(u + a) cos© + n(v + b) sine (2.1) V = -m(u + a) sine + n(v + b) cose (2.2) where a and b are the amount of translation in the horizontal and vertical directions, m and n the magnification factors in the horizontal and vertical directions, and 6 the angle of clockwise rotation. -X- For a detailed description of the mathematics and hardware required to produce the different matrices, see (3). 1 UNIT HORIZONTAL TRANSLATION TO THE RIGHT INPUT PATTERN 1 2 3 4 5 8 4 1 01 000 000 1 1 1 o O UTPUT PATTERN 01 020 034 ♦k COEFFICIENT MATRIX -*-k Figure 2.1 Translation Example 2.2 Pattern Recognition When in the pattern recognition mode, the display of Trans formatrix shows at a glance when a predetermined subject has been found. Pattern recognition is accomplished by consecutively displaying the summation of the 25 products produced by multiplying the 5 by 5 coefficients, selected by the operator, times each 5 by 5 subsection of the input pattern. The summation displayed at the output points (k,i) represents the center of the 5 by 5 input subsection sampled. Figure 2.2 shows the coefficient array required to detect the letter P. Switches in the coefficient array, when set to a +1, represent the image to be detected, in this case a P. The remaining switches are set to a negative number, in this case -.9, so that the sum over the 25 switches is zero. By setting the switches, using the above rules, the output pattern shown in Figure 2.2 will be produced. 2.3 Two Dimensional Fourier Transform Trans formatrix, in the Fourier Transform mode, uses all of its parallel computational ability in order to perform the two dimensional Fourier Transform at standard television rates. Once an operator is trained in the interpretation of Fourier Transforms, he should be able to detect periodicity or regularity, i.e. made structures, easier from the Fourier Transform of the picture than from the picture itself. Transformatrix will display any one of the three functions {|F(k,i)|, |Re[F(k,i)]|, |lm[F(k,i)]|} given by: INPUT PATTERN ••• • • • •••• 5X5 COEFFICIENT ARRAY 1 1 1 1 -.9 1 -9 -9 1 -9 1 1 1 1 -9 1 -9 -3 -.9 -9 1 -9 -9 -9 -.9 VALUES SET BY OPERATOR OUTPUT PATTERN -2 -3 2 1 1 -3 -6 2 -1 1 1 12 5 3 -2 4 1 1 2 6 3 2 Figure 2.2 Pattern Recognition Example 1 31 31 ki + 9\ F(k,i) = ± .Z Q X Q x ± . • exp[-25ti( K1 3 + / J )] (2.3) Fe[F( M )] = ± .| J x.. . e oa[a»(S^ii)] (2.4) 1 31 31 ki + fl Im[F(k,i)] = ~ .E d | x ± . • sin[2n( K1 3 + / J )] (2.5) Applications of the Fourier Transform are shown in Appendix A. 3. SYSTEM DESCRIPTION Transformatrix is a 102^- channel parallel processor which performs the linear transform: 31 31 y ki - i& jSo b ijki * *ij (3-D i, j, k, I = 0, 1, . . ., 31 where x. . represents the intensity of a quantized spot (ij) on the input image, b. „ represents the (k • £) matrices of (i • j) coefficients, and y . represents the intensity of a quantized spot (ki) on the output image. This chapter describes the system required to perform the linear image trans- formation, equation (3.1), at television rates. 3.1 Block Diagram The system block diagram of Transformatrix is shown in Figure 3«1- Two 32 by 32 input channels, one containing voltages representing the x. . input intensities and the other containing voltages representing the b. . coefficients, lead into the stochastic processor. Each of the x. . voltages is converted to a Synchronous Random Pulse Sequence (SRPS) by comparing the voltages with Quantized Random Analog Signal (QRAS) number one, using voltage comparators C^ „ to CL n „, . At the same time the b. ,, „ voltages are converted 0,0 31,31 ijki to SRPS's by comparing the voltages with QRAS number two, using voltage 2 parators C - to C . U, U 3-L, 3-L At this point in the processor, two simultaneous operations are .. representing the input image are multiplexed lessor section; OR'ed; integrated, and displayed on an a < 1 1 IE i "S I I 3 o ' < 3 h cd •H Q o o H pq H CD fe 10 oscilloscope (upper channel on Figure 3«1)» This displays to the operator the input image seen by the photo processor. Second, the SRPS's representing the input image and the SRPS's representing the coefficients are multiplied; summed; integrated; and displayed on a second oscilloscope (lower channel on Figure 3.1) • This displays to the operator the transformed image. We have, thus, produced two displays. One, whose point by point brightness, duplicates the input image; and the second, whose point by point brightness, depends on the linear transform. 3.2 Timing The basic timing for Trans format rix is dictated by the following three requirements : (A) The output display frame rate must^be the same as the frame rate of a conventional TV receiver - 30 frames /second. (B) The fastest economical digital circuits in integrated circuit form are transistor-transistor logic circuits with a maximum practical repetition rate of ten megahertz. (C) Transformatrix will display an output picture of 32 by 32 resolution. Since Transformatrix will display 1,024 output points at a rate of ) frames /second, a new output point will be calculated every 32-552 micro- seconds, or at a rate of 30. 72 kilohertz. Thus we need a master clock frequency of . I megahertz, which gives us 325 time slots per stochastic . display, there is no interlacing; thus, the frame and field rates 11 Figure 3«2 shows the timing and gating pulses which are derived from a 9*98^ megahertz multivibrator, master clock. A counter^ ' then produces an output pulse - point clock - for every 325 master clock pulses. Monostahle multivibrators are used to produce a shift clock; a reset clock; and a blanking pulse from the point clock. 12 f ; 9.984 m.Hz. 1 lUlil^^ -» T: 100.16 N.se-c. f r 30.72 k.Hz. Hrnf^^irnriF MASTER CLOCK T: 32.552U.sec POINT CLOCK .1 32.452 n n n n f b SHIFT CLOCK n fn In In In * RESET CLOCK XO 31.552 rb BLANKING Timing Diagram 13 h. STOCHASTIC PROCESSOR In order to perform the linear transform at television rates, the following requirements must be met : (A) The summation of 102^ products must be performed in 32.552 microseconds at minimum cost. (B) The accuracy of the answer must be near 5^>> in order to allow twenty gray levels on the output display. When the construction of Trans for matrix was begun, digital and analog multipliers, of the accuracy and bandwidth required, were very expensive. Thus, in order to keep costs down, random pulse sequence methods were chosen to perform the 102U parallel multiplications. This section describes synchronous random pulse representation; conversion of analog signals to random pulse sequences; multiplication of random pulse sequences; and conversion of random pulse sequences back into analog signals. h.l Synchronous Random Pulse Sequence Representation The probability that a pulse from a random pulse generator is present in a fixed time slot is the stochastic sequence representation of an analog variable limited to the range to 1. But, by analyzing one time slot, which contains either a "1" or "0", the value of the analog variable cannot be determined. Thus the analog variable must be determined by averaging the stochastic sequence over a number of time slots. In other words, we represent the analog variable by the number of time slots that contain a logical "1" divided by the total number of possible time slots. According to reference (5), page 13^, the maximum contrast ration between small closed areas is about 20. Ik k.2 Synchronous Random Pulse Sequence Multiplication The Synchronous Random Pulse Sequence (SRPS) multiplier is the only element to emerge from the studies '> * 'of SRPS arithmetic operations that has no inherent error other than the probabilistic nature of the answer being produced. In SRPS multiplication, the product of two SRPS signals is obtained with a digital "And" gate. When two independent SRPS signals, with duty cycle u and u p , are fed into an "And" gate (as shown in Figure 4.1), the output of the gate is given by: T -£ / u 3 (t)dt (4.1) U 3 '0 = P{u (t) has a pulse in a time slot} = P{u (t) and u (t) both have pulses in a time slot} = P{u, (t) has a pulse in a time slot} x P{u (t) has a pulse in a time slot} = U l ' U 2 4.3 Quantized Random Analog Signal Generation Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin. -- John VonNeuman (1951) An analytical and experimental study of plasma breakdown diodes as (q) xrces was made. ' ' It was finally determined that the high repetition rate and mal stability (required for Transformatrix) would not be obtained ■-•-emitter junction of transistors tried. Also, the 15 w o TO r in w ■N 3 1 51 ^ T- O «- O in: c: CM + r> □ CO en +10 + n o •H -P 03 o •H H Ph •H -P CD O I 0) CQ SEQUENCE NUMBER J_ 1 1 2 3 4 1 5 1 6 7 1 8 9 10 1 1 1 12 13 o 14 15 1 16 17 1 18 19 1 20 1 2 1 1 22 23 1 24 1 25 26 2 7 28 1 29 1 30 1 31 1 1 1 Figure J - _2_ STAGE A- 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -5- 1 1 1 1 1 1 1 1 1 o o 1 1 o 1 1 1 1 1 o o 1 5 Stage Pseudo Random Bit Generator 19 the required feedback, exhibits the properties represented by the following truth table. Input 1 Input 2 Output 1 1 1 1 1 1 Table 1. Truth Table for a Modulo Two Adder Assume, as shown in Figure ^-.3, that initially the shift register contains all "l's". Then, as the clock pulses enter the register, the modulo two adder samples the second and fifth stages of the register to determine whether to feed a one or zero into the first stage. Reference (10) describes an algorithm for selecting which stages to feedback in order to obtain maximum length sequences. Maximum length sequences, obtained in the manner described above, behave like the random sequences obtained by independent trails with Probability [0] = Probability [1] = 1/2. In particular, each maximum length shift register sequence can be shown to have three significant "pseudo randomness" properties : (A) In each period of a maximum length sequence, the shift register takes on every possible binary number, except the all-zero state. 20 (B) In every period of a maximum length sequence, one-half of all the runs (subsequences containing only 0's or only l's) are of length 1 (0 or 1); one-fourth are of length 2 (00 or 11), etc.; and for each run of 0's, there is a run of l's of equal length. (C) If -we let successive output bits (0 or 1) be denoted by a , a^, ..... then YOO = -f [k = 0, ± (2 n - 1), +2(2 n - 1) ... . 2-1 2 n-2 otherwise (h.2) 2 n - 1 the discrete autocorrelation function is periodic and has only two values. In order to convert an analog signal to a Synchronous Random Pulse Sequence (SRPS), a Quantized Random Analog Signal (QRAS) must be produced from the pseudo random bit generator. Considering the binary word Y = (Y-, Y . . . Y ) as a subset in the pseudo random sequence, a digital to analog converter will generate the QRAS pseudo random whole-word fractions ( -Vo b i Y i • • • Vi\-i>> (-Vk b i Y k + i • • • Vi Y 2k + i> • • • • The method by which a new bit is presented to the pseudo random shift register and the way each bit shifts right one register for each clock pulse causes very strong local nonrandom subsequences to be formed. This is demonstrated in Table 2, where the results of five runs of 325 consecutive sequences with n = 33 produce "random" numbers from to 31 using the following digital to interger conversion. uge 1) + 2.0 x (Stage 3) + h.O x (Stage 5) + 8.0 x (Stage 7) • :tage 3 (^.3) 21 OCCURRENCES LEVEL 1 -2. 3 _4_ Jl 8 2 17 5 9 1 9 5 12 7 9 2 11 9 12 10 11 3 17 10 12 9 5 4 10 9 13 10 10 5 9 12 14 12 10 6 9 7 15 14 6 7 7 6 5 8 12 8 11 5 12 9 8 9 8 11 8 12 9 10 10 8 9 9 a 11 8 11 8 12 9 12 11 11 15 12 9 13 8 12 6 6 9 14 12 13 8 12 11 15 11 15 9 11 21 16 10 13 18 12 17 17 9 10 12 9 13 18 8 12 11 12 9 19 7 5 8 10 11 20 11 7 6 7 5 21 11 12 6 9 14 22 9 12 8 12 6 23 15 18 10 11 10 24 8 9 12 8 13 25 15 10 11 13 7 26 12 12 6 7 11 27 8 17 10 14 8 28 10 e 9 13 13 29 10 12 7 15 3 30 10 11 6 8 11 31 13 11 10 7 18 Table 2. 325 Sequences of a 33 Stage Pseudo Random Bit Generator 22 Thus we see from Table 2 that every- sequence is biased. Even though these sequences are satisfactory for communication testing and transfer function analyzers. I 11 ) > ( 12 ) > (.13) , (14) , (15) , v 16) they wlll cause an error in SRps multiplication . Before discussing error analysis, let's look more closely at SRPS multiplication as described in 3-0. A voltage comparator, Figure h.k, compares an input signal with a QRAS to produce a Synchronous Random Pulse Sequence. The required QRAS is generated by a pseudo random bit generator, followed by a digital to analog converter, as in Figure 4.5- Two of the QRAS characteristics may be defined as probability densities. First, over a given number of time slots (325), each QRAS level may have a different frequency of occurrence. Second, given specific time slots, the QRAS is a random sequence of levels. The statistics of the Synchronous Random Pulse Sequence are affected by both of the above probability densities. Since the likelihood of any QRAS level and the positional time alignment of any u, (t) and u^(t) are produced by different mechanisms, they be considered as independent. Thus, : (t) has a pulse in a time slot] = P[A11 QRAS levels are equally likely] x P[u, (t) and u, (t) have pulses in the same time slot] (4.4) bh the first term an error term; and the second term the SRPS multiplication '4.1) . The following two methods may be used to eliminate the error : 23 < QC O UJ > UJ z UJ X I- I- o > in > o > CO UJ CO -J Q. O Q Z < q: CO O o cr x o o CO cc UJ > o o >■ ^ CO UJ UJ o < CO H _J o > CD Q o •H W a o o co Ah cn w o •p -p O > Pi ft c -J- 2k CLOCK i > fftN r n o o B a —2 _©_^ r» v W w R w n w K w s Q S 5 S 5 s 5 s 5 l^~ yr — ( 8 4 2 16 1 DIGITAL TO ANALOG CONVERTER urn TAKI 1 ' ORAS QRAS TIME QUANTIZED RANDOM ANALOG SIGNAL Figure k.5 QRAS Generation 25 (A) Allow the number of time slots (m) to be very large so that each QRAS level is equally likely. (B) Tailor the QRAS signal so that each level occurs exactly a given number of times over (m) time slots. Both methods make P[A11 QRAS levels are equally likely] tends toward one and the multiplicative error term drops out. In Trans formatrix, with m equal to 325 and n = 5 (N = 31), 16 levels occur 10 times and 15 levels 11 times. From the frequency test of (15), this makes the P[A11 QRAS levels are equally likely] greater than .995* But if we consider run number 3> from Table 2 and shown in Figure k.6, (according to the frequency test as above) the P[A11 QRAS levels are equally likely] is only about . 30 which is a large error term in (U.U). To conclude, pseudo random bit generators offer the following striking advantages : (A) Pseudo random sequences are produced by reliable and inexpensive digital circuits. (B) The shift register can be reset at any time to repeat a "random" experiment . (C) Digital to analog conversion of the shift register contents yields a Quantized Random Analog Signal. (D) By proper decoding of the shift register contents, each level of the QRAS may be individually set. n-1 (E) Over the maximum period 2 , while using all n stages of the shift register as output, the all zeroes state can never occur. 26 C\J — f 1 Or j K c Q 1 J K c 9 J K c Q a 3 J K C a 4 J K C Q 3 c J o K Q [L. V STAGE STAGE STEP 1 2 3 4 5 6 STEP 1 2 3 4 5 6 1 1 1 1 1 1 1 33 1 1 1 2 1 1 1 1 1 34 1 1 3 1 1 1 1 1 35 1 1 4 1 1 1 1 36 1 1 1 5 1 1 1 1 37 1 1 1 1 6 1 1 1 38 1 1 1 1 1 7 1 1 1 39 1 1 1 1 8 1 1 1 1 40 1 1 1 1 9 1 1 1 41 1 1 1 1 10 1 1 1 42 1 1 1 11 1 1 1 43 1 1 1 12 1 1 1 1 44 1 1 13 1 1 1 45 1 1 14 1 1 1 46 1 1 15 1 1 1 1 47 1 1 16 1 1 1 1 1 48 1 1 1 17 1 1 1 1 49 1 1 18 1 1 1 1 50 1 1 19 1 1 1 1 1 51 1 1 20 1 1 1 1 52 1 1 21 1 1 1 1 53 1 1 22 1 1 1 54 1 23 1 1 1 55 1 24 1 1 1 56 1 25 1 1 57 1 26 1 1 58 1 27 1 1 59 28 1 1 1 60 29 1 1 1 1 61 1 30 1 1 1 62 1 1 31 1 1 1 63 1 1 1 32 1 1 1 1 1 1 1 1 Figure h.Q 6 Stage Pseudo Random Bit Generator 7S O IO *t e N U X u 9 o IT E Ul LU K <5UM S- A TZ C J IO lo >y3 A £J 42 S L— <» rzr o 3 * tzt 32 I r e *o o -p 0) o -3- •H 33 10 inch by 18 inch printed circuit cards. There are no conventional digital to analog converters available that can provide the slew rates, settling times or current driving capability required of the QRAS signals. Thus, the following special circuits were designed. The output of the pseudo random bit generator must be converted to a 32 line representation because the QJIAS levels are set to compensate for non- linearities in the input picture voltages and coefficient voltages. When each of the 32 lines represents a distinct level, a voltage spike is produced when- ever transferring from one level to another. This voltage spike is caused by the falling and rising times, Figure 4.10. Since the QRAS signal contains randomly occurrring levels, the signal may either decrease or increase at any transition, making signal tailoring impossible. One solution to this problem would be to decode the 5 bit pseudo random generator outputs with a digital "shorting switch". The "shorting switch" decoder produces an output on line one whenever there is an input on lines one through 31? an output on line two whenever there is an input on lines two through 31? and so on. By using type D storage flipflops to store the decoded signals for one 100. 16 nano- second period, one-half of the previous time period may be used to perform the "shorting switch" decoding. In this way, four series logical gates may be strung without their combined delay times adding up to more than 50. 08 nanoseconds. The schematic of the OJIAS "shorting switch" decoder is shown in Figures 4.11 and 4.12. After the pseudo random bits have been decoded by the "shorting switch" decoder, each digital to analog driver provides approximately the same current to the summing network. Now as the QMS changes levels, either more or less analog drivers supply current to the summing network and no voltage spikes are produced. 3<* k I o M •H pq w 0) •H ft CO 0) -p H CH O W 17 F()RMAT(5F10.1 ) WKITF (6 t 31) VM,RM,VN,RN,FR 31 FORMAT (1H1.5E20.7//) GD=0 .0 no 10 1=1,32 VI) ( I )= ( V0( I )/.97)-.04 G( I )=0.0 10 R ( I )=0.0 DO 20 1=1,32 M=I-1 F= (VM-VO( I ) )#FK/VO( I ) R( I )=F G ( I ) = 1 . / R ( I ) IFU-1 )91,92,91 92 GPU )sG( I ) GO TO 93 91 GPU )=GU )-G(N) 9 3 FG = l ./GPU ) RP( I )=FG-RM RA=R( I ) GA=G( I ) GZ=GP( I ) RZ = RP( I ) VA = VO( I ) WRITF(6,21 )VA,RA,GA,RZ,GZ 21 FORMAT (5F25. 7 ) 20 GD=G0+1 .0/ (RZ+RN) GB(1 )=GD ^RITF(6,72 ) 72 FORMAT!//) 00 50 J=l,5 K ■ J + 1 GB(K )=0.0 WRITE (6,31) VM,RM,VM,RM,FR 00 40 1=1,32 N= I - 1 IF ( 1-32 )84,85,84 HA GB( J )=GB( J )-l .0/(RP( I )+RN) FB«GB LADDER RESISTOR 00132 Figure 4.15 Schematic and Model of the Resistive Ladder Driver kl ORAS COEFFICIENT INPUT LEVEL CHANNEL CHANNEL 1 .5801 .1590 2 .7 406 .4435 3 .9011 .6 845 4 1.0613 .9093 5 1.2217 1.1237 6 1.3823 1.3304 7 1.5429 1.5310 8 1.7024 1.7268 9 18627 1.9183 10 2.0235 2.1063 11 2.1 844 2.2911 12 2.3451 2.4731 13 2.5060 2.6526 14 2.66 70 2.8298 15 2.8279 3-0049 16 2.9895 3.1 780 17 3.1495 33494 18 3.3112 3.5192 19 3.4 730 3.6873 20 3.6 349 3.8541 21 3.7 968 4.0194 22 3.958 7 4.1835 23 4.1206 4.3464 24 4.2830 4.5081 25 4.4457 4.6687 26 4.6078 4.8283 27 4.7700 4.9868 28 4.9323 5.1444 29 5-0947 5-3011 30 5.2570 5.4569 31 5.4192 5-6120 32 — 5-7661 Table 3. QRAS Levels for Coefficient and Input Picture Channels k2 INPUT Q3 OUTPUT Q3 Figure k.l6 Schematic of National NH0002 43 4.4 Conversion of Voltages to Synchronous Random Pulse Sequences A voltage is converted to a Synchronous Random Pulse Sequence by comparing it with a Quantized Random Analog Signal. Assuming the voltage is between and 5 volts and the QRAS has 32 levels with the value of the voltage at each level independently adjustable, then each level of the QRAS has a probability of 1/32 of occurring. Thus, with the inputs of a voltage comparator, Figure 4.4, connected so that when the input voltage is greater than the QRAS, the output is a logical "1"; the greater the input voltage, the higher the probability of an SRPS pulse appearing in a time slot. The accuracy of this conversion process is determined by: (A) the voltage comparator offset. In Transformatrix, a 5 milli- volt worst case offset takes up about 3*1% of "the level separation. (B) the number of quantized levels in the QRAS. In Transformatrix, 32 levels gives us a worst case accuracy of 3«1$>« (C) the statistical properties of the QRAS generator. See section 4.3.1. 4.5 Stochastic Processor Card A picture of the stochastic processor card in its tester is shown in Figure 4.17 . This card produces two outputs: (A) A resistive summing differential amplifier provides the summation of 32 multiplications. (B) A 32 input "NOR" gate provides a multiplexed version of the parallel input image intensities . One of the 32 identical stochastic processor cells is shown schematically in Figure 4.18. Each cell contains two 7 10 voltage comparators, kh Figure h 17 Stochastic Processor Card s o ^ (/> H 3 O - 1 o 1 _J < ____ 1 f > H Z 1 UJ Q 1 en ^~ K CM 1 Z IO < OR CONST CVJ -• OR SITIES »- z 0) V\z o o < < tfw UJ — q: Lj£ CONN SFORMAl s- Y V r 4 is 8g < > 1 ^ 2 z "■• < cr »- v v 4) u ^< o 3 b 1 2 ».. * + E ^ ill jll^i - ') * <*| " '» (4.17) n n Analyzing the second term where i ^ j, E[(y. - y) x (y. - y)] * E[y.y.] - E[y.y] - E[y..y] + E[y 2 ] (4.19) Using the property of the SRPS's that over a 325 time slot period the probability of a pulse occurring in a specific time slot is independent of any other time slot, leads to E[y. - y) x (y - y)] = E[y ] x E[y ] - yE[y ] - yE[y ] + y 2 (4.20) = y 2 - y 2 - y 2 + y 2 = o (4.21) 49 Thus, equation (4.18) becomes 4n " -T Ja'toi " y)a J (k - 22) 2 e: 1=1. T) n Again, as in (4.11), taking the 2a.™™ variation as the accuracy of the conversion process and o from (4.10) P 1 o_ p Error = 2c EST = — ^- = 2 ^< 1 "/^ (4.24) (n) 2 (n) 2 which is the same as equation (4.11). For Transformatrix, with n = 325 time slots, we get 1 Error ($) = 11.1 [p(l - p)] 2 (4.25) which is plotted in Figure 4.19. 50 ERROR 25 .50 .75 1.0 ■re k.l'j Percentage Error Versus SRPS Value 51 5. INPUT IMAGE PROCESSOR Transformatrix, in order to process pictures from a television receiver or slide projector, must convert a quantized 1024 point input image into 102U parallel output voltages. Because of the low light level produced by the Cathode Ray Tube, the input image processor is designed for maximum power transfer from the television screen; and the intensities from the slide projector are then tailored to this low light level. This section describes the characteristics of a television receiver; cadmium sulfide photoconductors; a computer program for simulating the television-photoconductor dynamics; and the input image processor card. 5 . 1 Review of the Characteristics of a Television Receiver A standard television picture consists of a 525 line scanning format. With the viewer facing the monitor, the lines are scanned horizontally from left to right and vertically from top to bottom. Since the 525 horizontal lines are scanned at a rate of 15,750 lines per second, the duration of each line is about 63. 5 microseconds. The entire picture, called a frame, is displayed 30 times per second, or it takes 33 • 3 milliseconds to scan a whole frame. Each frame is divided into two interlaced fields, designated as even and odd. By starting the scanning beam at a different place for each of the fields, the lines of one field are placed halfway (interlaced) between those of the other field. Thus, each field is scanned in 16.7 milliseconds. 52 5.2 Conversion of a Scanned Television Image to Parallel Voltages Two synchronous and one asynchronous method of converting a scanned television image to parallel voltages are described below. 5.2.1 Synchronous Conversion with Digital Storage Figure 5«1 shows a video to digital converter being gated to a five bit flip flop memory by counters synchronized with the television's vertical signal. The information stored in the flip flops is then reconverted to an analog voltage by a digital to analog converter. 5.2.2 Synchronous Conversion with Analog Storage Figure 5-2 shows a high speed gated sample and hold circuit which stores the image for one field. The sample and hold circuits are gated by counters synchronized with the television receiver. Both synchronous methods are very expensive to implement and take up a large amount of space. 5.2.3 Asynchronous Conversion Using Photoconductors By using the asymetrical relaxation characteristics of a photo- conductor to dynamically store the image from a cathode ray tube, an in- expensive method of converting the light images to voltages, and storing the image information, has been used. This method of storing analog information is similar to the method of reference (17) which stores binary . 53 < 3 CD o < O »- ac Hi Z o u u o •p ra -P •H bO •H Q X! •P •H o •H W > o o CO T u z > o § Sh o CO I •H o UJ o > r T UJ Q ^ O to O _l .j < * < z c\j z o < to Hi **«. to LU _i Q. CO LU < to Z -1 < O I Z o u ■5? 1 o Ltl Q T U z > to 0! ?H O -P CO o H ct) < +3 >H o •H ra 0) > cs o o w o a o $-i .3. u g, co CM LTN a) bo •H 55 5.3 Construction of Photoconductors The essential elements of a phot oconduc tor are a ceramic substrate, a layer of photoconductive material, electrodes, and a moisture-resistant enclosure. A photograph of a photoconductor is shown in Figure 5-3« The photoconductive material used in Trans formatrix is cadmium sulfide which is treated (doped) with various activating metals, such as chloride and copper, for increased sensitivity. The metalic electrodes on the surface of the photoconductor are formed by evaporation through a mask. Tin and indium are the commonly employed electrode materials because they produce ohmic contacts, A drawing of the surface of a simple photoconductor is shown in Figure ^>.h. The operating voltage is applied between the electrodes, which is across the dimension t, of the photoconductive surface. The dimension L determines the number of possible parallel paths across which photocurrent flows. Thus, for a given operating voltage and light level, photocurrent is proportional to L (resistance a l/L) . The dimension L is extended by folding back or couibweaving the photoconductive material. Although the photocurrent for a given operating voltage and light level can also be increased by decreasing the dimension t (resistance at); this reduction also decreases the maximum voltage which can be applied between the electrodes. 5.^ Physics of Photoconductivity For a non-degenerate semiconductor or insulator, the conductivity c is proportional to the density of charge carriers. The relationship is a = q(u. n n + u. p p) (5.1) where n and p are the densities of the free electrons and holes, and |a and 56 it '^conductor 57 CADMIUM SULFIDE DEPOSITED METAL ELECTRODE NO. 2 DEPOSITED METAL ELECTRODE NO. 1 Figure 5.U Drawing of Simple Photoconductor 58 ii are the respective mobilities, while q is the electronic change. By using P the energy band picture, it is assumed that energy is required to raise electrons across the band gap to form free electron-hole pairs. With the above energy supplied thermally, the electrons and holes created are called equilibrium carriers and the corresponding conductivity, equilibrium conductivity. Any other form of energy supplied is mainly retained by the electrons and does not seem to effect the crystal lattice. Thus, these carriers created by energies other than thermal are called non- equilibrium carriers and the corresponding conductivity, non-equilibrium conductivity. When the energy supplied comes from photons, the change in conductivity is called photoconductivity. When a photoconductive material is excited by photons with energies larger than the band gap, carriers are generated at a rate corresponding to the excitation intensity. In the steady state, the excess carrier density reaches a final value when the generation of carriers is balanced by a reverse process known as recombination, which is believed to be dominated by Shockly, Read and Hall -- SRH -- centers. ''^ These SRH centers are discrete energy states which exist in the forbidden band as a result of defects in the crystal structure. The interactions between electrons and 2S and SRH centers are characterized by four different processes (see Figure 5.5 • 'mpty center may capture an electron from the conduction banc. -oss a, or it may emit a hole into the valence band, as in . and a filled SRH center may either emit an electron into the as in process b, or it may capture a hole from the valence bana . 59 LU UJ > C o U P o W u p G 0) o co o u ZZ o< UCQ CO or uj q:z xuj i/)U LU U z _ uj 5 _J z << > CD CD •H 6o Since SRH centers play a dominant role in non- equilibrium conditions for most phot oc on due tors, understanding their characteristics will be essential to understanding photoconductors. From the four basic capturing and emitting processes, an electron, after being captured by an SRH center, would either recombine by capturing a hole or be thermally emitted back into the conduction band, both of these possibilities having defined probabilities. The SRH centers may, therefore, be divided into four groups. Those centers, where the probability of a captured electron being recombined is higher than the probability of a captured electron being re-emitted back into the conduction band, are called electron recombination centers. These centers, where the probabilities are reversed from those above, are called electron traps. It is apparent that the energy level of the center determines whether it acts as a recombination center or a trap. Thus, the energy level, where the probabilities of recombination and re-emition are equal, is called the demarcation level. The forbidden band can, therefore, be divided into three regions by the demarcation levels as shown in Figure 5.6. The SRH centers located in region I and II act as electron and hole traps, and the SRH centers in region III act predominantly as recombination centers. From reference (20) it is seen that the transient processes of photoconductivity are closely related to the location of the SRH centers. ' the centers are located near the dark Fermi level, they are predominantly recombination centers and the transient response has the same rise and fall times. However, if the average level of the SRH centers is moving toward ; . :tion band, the characteristics of the centers shift toward more ping action and the lifetime of free electrons is increased. This b, thus, making the rise and fall times more . 61 c UJ w U 0) -P PI (IJ CJ> « CO Ch o G O •H -P Oj o •H Ch •H w w H O LA 0) ■H P«4 z h- u zz o< UJ u z LU < > < CO 62 The above analysis gives a good picture of the physical process of photoconductivity; but as yet has not given practical mathematical results. Thus in the analysis and design of the input image processor, the photo- conductor 'will be modeled by its black box-system-characteristics either given by the manufacturers or measured in the laboratory. 5.5 Photoconductor System Characteristics In order to apply photoconductors effectively, the spectrum response nonlinear transfer function, and asymetrical transient response must be thoroughly understood. 5.5-1 Spectral Response To obtain the maximum power transfer from the cathode ray tube phosphor to the photoconductors, their frequency spectrums must be matched as close as possible. The power transferred from the phosphor to the photo- conductor is given by Q = [ 2 (E x ) x S(\)d\ (5.2) 1 where Q is the power at the photoconductor, (E, ) is the spectral density of the phosphor, and S(\) is the spectral sensivity of the photoconductor, reference 21). Figure 5*7 shows that the spectral response of the P-U .as two peaks: One is located at about .kk microns (blue) and the •■■•ted at , .56 microns (yellow). Defining the phosphor decay Howing removal of excitation, during which the luminance F its initial value, the blue component has a decay yellow one a decay time of 60 milliseconds. H O < a. _i i/> LU W a: ce 63 < o •H w •H > 0) H - -p ( o r— i—i TJ S^ o ^^ o o LU o -p 1 — o 2: £ oo i/) ir\ -or 0) CD & hO •H P^ O (D 00*01 00 "8 00'9 OO'Ti 00"2 00*0° 66 by the manufacturers of the photoconductors. The response time versus intensity when plotted on log-log paper is very nearly a straight line. Thus Y = BX" 1 (5.1+) ■where Y is the time constant in milliseconds, X the intensity in foot-candles, B the time constant at an intensity of one foot-candle -- [Y(X=1.)], an d m = log[Y(X=l.)] - log[Y(X=.l)] (5.5) The characteristics of the seven photoconductors to be analyzed in Section 5.7 a^e given in Table k. 5.6 Input Image Processor Card A picture of the imput image processor card with its tester is shown in Figure 5«9« This card provides the following functions: (A) Converts the scanning input intensities from a television receiver to 1024 parallel voltage lines. (B) Corrects for variations in R of the transfer function. (C) Provides low impedence line driving. -. of the 32 identical input image processor cells is shown schematically "igure 5-10. 67 00 N CD co ro CO GO cd flO CVJ N If) co CO in N if) ro (0 to if) CO o U O ro CO CO s o O CO w CJ •H +3 w •H Ph CD -p o cci O CO O CO oo in CVJ CVJ 00 ro a CO u UJ O 66 Figure . I nput Image Processor Card in 69 - {/) — ^ a: o _j < • o i— i »- *■* Z tn LU > O Q CC p > u oH VSN «■ °% 05 1* xo *0 or ii Til Z •< ' ^^ > *1 ~H ^ \y L -v s Hi' + V- V CONNECTOR o h- o LU CO o: o CO CO UJ o o Thus with V a standardized voltage 5 the variation in R may be canceled by adjusting B^,. Even though adjusting 102U trimmers is a tremendous job, a tester was designed and built which allows the adjustment to be completed rather quickly. The tester consists of a block box with a light bulb at one end and a slot for inserting the input image processor card at the other end. Each output of the processor card is connected to one side of a voltage comparator; with the other side connected to a voltage standard. Thus, when the trimmer is adjusted so that the output voltage, corresponding to a given intensity on that photoconductor, equals the voltage standard, the voltage comparator changes states, lighting a bulb. Using this tester, all 32 -3 on one processor card may be sequentially adjusted very quickly. 71 u CD P > a o o CO P-, « CO o -p >> -p •H W fl (D -P c H 0) 2 •H P-h to > 72 5.6.2 Linearizing the Photoconductor Transfer Function .Qk The nonlinear response -- (I)" -- of the photoconductor is linearized during the voltage to SRPS conversion process, Figure 5.11. With the photoconductors located at a distance of about three feet from the cathode ray tube of the television receiver, the light intensities from the cathode ray tube should vary between .1 and 1.0 foot-candles. Also, the comparator has a maximum rating of +5 volts between its input terminals; and +7 volts between either input terminal and ground. From equation (5*6) with V R /R = 5.0^3? V is equal to .8^3 volts at .1 foot-candles and equal to . -3 volts at 1 foot-candle, giving the greatest noise margins while not exceeding the maximum ratings of the comparators. Using the definition that the SRPS is a logical "1" whenever V is greater than the QRAS, the 32 nonlinear levels for QRAS that linearize the intensity to SRPS transfer function are given by: ( ^ )levels . a w-g + -gi^af + ■^ir 8 \ (5 . 7) N = 0, 1, 2, . . .,31 The above QRAS levels are shown in Table 3' 5»7 The Dynamic Response of Photoconductors Illuminated by a Television ;iver This section provides a mathematical or computer model for • the dynamic response of a photoconductor when illuininated by a This model will then be used to determine the optimum itrix. Seven commercially available photo- their spectral response and asymetrical transient 73 behavior, are compared. Because the dynamic responses are calculated in the intensity domain, the following terms, which are analogous to terms used in describing the operation of a motor, are coined. (A) Effective Intensity (IN ) - an instantaneous intensity which produces the same effect (conductance of the photo- conductor) as a steady state intensity of the same value. (B) Counter Intensity (IN„ ) = the effective intensity which is stored in the photoconductor as trapped carriers (Section 5.h) or as an effective conductance which is measured at an instant of time. (C) Stimulus Intensity (IN ) = the effective intensity of the source or in our case tne phosphor of the television screen. (D) Working Intensity (IN n ) = the difference between the stimulus intensity and the counter intensity. IN is forcing the conductance of the photoconductor to follow the intensity changes of the stimulus. 5.7.I Response for Simplest Television Receiver Model Since Transformatrix will contain a 32 by 32 array of photoconductors, the simplest model of a television receiver is one with 32 scanning lines per frame. Since the beam scans each field in 16.667 milliseconds, it is affecting the active area of each photoconductor for a maximum of 16 microseconds. With the active element containing slightly less than half the area of the encapsulated mounting, Figure 5.U, the beam is affecting the active area of photoconductor for a minimum of 6 microseconds. The dynamic response of the system has three regions as shown in Figure 5 .12. In region I, the electron beam is energizing the phosphors of the television screen to produce an intensity -- IN -- of A foot-candles. The intensity rise time of the phosphor, when stimulated by the electron beam, is almost instantaneous because of the tremendous amount of energy in the electron beam. Thus, in this analysis, the intensity response to the electron 7^ Ld > UJ o LxJ O I- cr o i- o O z o o o h- o X u. o UJ CO O a. to UJ a) > ■H <1J O 0) cr; > EH O -P fH o -p o T* C O o o -p o XI On and the response for the beam being on the photoconductor for 6 microseconds, Figure 5-lj, are shown. Because the difference in these two figures is unnoticeable, does not matter at this time whether the rectangular area of the photo- ■ . Figure ' . . s horizontal or vertical, with respect to the scanning 77 /*ID PS = 1 203, r)FPT = OCS,Cni)F = HRDWRE,NAMF = MARVEL, /* LINFS=6000,360=2.»CALC0MP=YES // FXFC FOKTLKFO //Ff'KT.SYSlM !)[) * DIMENSION XA(4000) ,P(4000) ,TX<2> tTY<2) C C LUMPFO PHOTO-CONDUCTOR RFSPONSF TO T V , FXPONFNT I AL c CALL CCP1PL ( 1.0, 1 .0» -3) TX ( 1 )=0.o T X ( 2 ) = 2 . TY ( I )=(■.() TY(2.)=1 .0 SO KFAO ( S, 51 ) A,TA,TH,RA,RB,0, HM •SI FORMAT (7F 10. 3 ) \l = <) .0 CALL CCP5AX (0.0,0.0, »T IMF -MILLISECONDS' ,-17,09.00,0.0,1 * ) CALL CCP5AX( 0.0,0.0, 'ill IT PI IT VOLTA^F' , + 14, 5. <)0,U h = A* ( I .O+L/HM ) f',11 Til 4 3 A ?. H = A ^4 1 = ] 15 S=. 002*1 ■: = S + V R ( K ) = W YA=Yrt+ ( H-YK ) *( 1 ,0-FXP(-S/TA ) ) XA (K ) =M*YA**.H^ \f- ( S-KA ) 10 t 10, 11 111 f = I+l K = K + 1 Of) TO IS 1 1 .1 = 1 <=K + 1 YC=0.0 YD = YA T 7 = T A i»A = .() JH=1 2 5 U=.5*J X = M+ HA \/ = l-: + X P(K)=V Yrt = Yf)+(H*FXP(-X/02.00)-Y0)*( 1 .O-FXP ( -U/TZ ) ) XA (K )=0*YB**.84 IF(X-RH)20,20,21 ?0 I F ( JR-l )M ,M ,52 51 IF(YC-YB)30,30,3l 31 YO=YC T 2 = T H |IA = i I ,1=0 Figure 5.13 Program for Response to 32 by 32 TV System 78 JB=2 CM TO 62 40 YC = Yrt h? J=J + l K = K + 1 G('l TCI 2S ?A K = K + ] 40 CllMT INUH KA=K-1 CALL CCHM.N( P,XA,KA, 1, TX,TY) CALL CCP1PL ( 11 .0,0.0,-3 ) U() TH SO hNil) ..'. Program for Response to 32 by 32 TV System o a I; CM ro >> OJ CO (-( o <4H w d o ft w 0) bO ■H -JDbllDA LRdinO 60 T CO o Cj O - 3* O - tj s OJ o >> o & o -- o 01 CM 00 "" ~" CJ O 1 C_J 1 LxJ PQ o tn a> o 1 — i CO . - rj _J p? .J ft ►— ■ i w 2: 1 a) LU r; ,= * • I" UA

EH CM O m C.j • >> r -5 . ~ ,o o CO ^ C3 CM 2L m o u CJ lU o o en U O i — i o-l en. J C s: O ft w i 0) Ld (Xj r-,51 o ~ h- o H • l — CJ 1X1 LT\ with a photoconductor whose active area is ,2k inches long and whose center to center spacing is .375 inches, we have 5 television scan per field affecting each photoconductor. From studying the physical action of the photoconductor, as described in Section 5«3 3 "the photo- r when divided into 5 equal parts along the length L, looks like 5 i series each with the same intensity to conductance ; , each subsection of the photoconductor is excited /#I0 PS=1203,OEPT = r)CS,COOF = HRDWRE,NAMF = MARVEL, ^ /* LI NHS = 6000, 1*0 = 2. ,CALC0MP=YFS,REGI0N=348K,TYPE=CPU // FXfrC FORTLKFO //FORT.SYSIN nn * DIMFNSIUM XA(4000) ,P(4000) ,TX(2) ,TY (2 ) C C L 1 1 ,VI P F n PHOTO-CONDUCTOR RESPONSE TO TV,DFLTA C CALL CCP1PL ( 1.0,1.0,-3) TX( 1 )=0.0 T X ( 2 ) = 2 . TY ( I )=0.0 TY(? ) = 1 .0 50 KFAO ( 5, SI ) A,TA,TH,RA,RB,n,BM 51 FORMAT (7F1 0,3) V/ = 0.0 CALL CC PS AX (0.0, 0.0, "TIME-MIL LI SFCOMOS' ,-17,09.00,0.0,TX) CALL CC PS AX (0.0, (J. 0, 'OUTPUT VOL T AGF ' , + 1 4 , h . 00 , 90 . , T Y ) Y A=0 • K = l Fsl .O-FXH (-.002/TA ) G=HXP(-.l/2.9) 00 40 L = l ,10 rh(BM)44,42.41 4 1 R=A*(L/HM) GO TO 43 44 H=A*(1 .O+l./BM) (;0 TO 43 4 ? rt = A 43 1=1 1^ S=.002*I w - S + v/ P ( K ) = w YA=YA+(B-YA )*F XA (K )=0*YA**,84 IF ( S-KA) 10,10,11 10 1=1+1 K=K + 1 go to i s n ,i = i Yh = YA K=K + 1 YC=0.0 C = H JH=1 F = l ,f)-FXP(-.l/TA) 2S U=.1*J V = M + lj P(K ) = V C=C*G YH=YH+ (C-YH )*F XA (K ) =D*YB*#.84 IF (II-R3 )20,20,21 2 IF ( Jh-1 )M ,Sl ,f>2 SI IF ( YC-YH)30,30,31 31 F=l .0-FXP(-.l/TH) JB=2 Figure S. 20 Program for Difference Equation Response 86 GO TO 62 ^0 YC=YB 62 J=J+1 K = K + 1 GO TO 2 5 21 K=K+1 YA = YB 40 CONTINUE KA=K-1 CALL CCP6LN=0.0 TX(? )=200.0 TY( 1 >=0.0 TY(2 ) = 1.() CALL CC PS AX (0.0, 0.0, 'Dl IT PI IT VOLT Af,F • , + 1 4 , *> .00 , 40 .0 ♦ T Y ) CALL CCP5AX( 0.0,0.0,' T IMF-MILL I SECONDS • ,- 1 7 , 09 . 00, 0. 0, T X ) 50 REAO (S,S1 )A,0,RM,4,R,C,0 51 FORMAT < ^10.3) Y( 1 )=0.() Y(?)=0.0 Y( 3 1=0.0 Y(4)=0.0 P( 1 ) = ,063«3 P(2)=.l2 70 P(3)=.140S P(4)=.?540 YA=0.0 N A = 4 PA=.2S40 EC=EXP(-. 0635/2. 9) 0A=n/5.0 Of) 20 L = 1,1.0 nil 20 M = i,10 Ih(HM)44,42,41 41 CA=A-(L/HM) Gil TO 4 3 44 CA=A*< 1.0+L/HM) GO Til 43 42 f.A = A V3 00 20 M=l ,262 MA=NA+1 IF(CA-YA)31 ,31,32 31 IF(YA-. 03)34, 34, 3S 34 TH = C*.. 03**0 GO TO 7 •=> 35 IM YA-1.0)36,3 /,37 ^7 TR=C (.0 TO 75 36 TK = C*YA#*(0 75 F/ = .0S3 C )/TK-.()0201 , 5/(TB*TR) GO Td 33 32 IF(YA-.03)38,38,39 38 TA=B#.03**R GO TO 76 39 IF( YA-1. 0)70,71, 71 I\ TA=H GO TO 76 Figure 5.23 Program for Final Model 90 70 TA=B*YA**R 76 FZ=.0635/TA-.002015/(TA*TA) 33 YA=YA+(CA-YA)*FZ CA=CA*EC Y(NA )=DA*YA**,84 PA=PA+.0635 P(NA )=PA 20 COMTINUF DO 60 N=l, 26200 NA=N+1 NB=NA+1 NC=MB+1 Mf)=MC + l Y(N)=Y(N)+Y(NA)+Y(NB)+Y(NC)+Y(ND) KA=26200 CALL CCP6LN(P,Y,KA, 1 ,TX,TY ) CALL CCP1PL<0. 0,0. 0,-3) GO Tf) SO EN I") Figure 5 -2k Program for Final Model 91 o -- OJ Y '9 0) " r ^ : V o •H CJ ' — '■ > Q Sen in O -o ■.y. c CD w (_), a U_i o o > — tj w d-4 « 0) Q O Cm 0) w o ft w CVI 0) •H 33bi">DA lridino 93 o CO o o .. CO --J ri • — ' 0) "3 ' — ' o C-» \< •H • ' — > 0) ^ U o o 4h ' U-i Q) ■_» i - W O 1— H ti | O cy J ft t— H ^X cu • * — ' Q O '■ OCO Jh -Q o ,Z CH O 0) (_J ra UJ o o07 ft O ' — i CO cJ-J 0) PS cc_j: i , ^ ao cu lU. LT\ ,-,22 c ' CD 1 bO •H • 1— c CD ."jaunoA indino 95 6. INPUT IMAGE DISPLAY CHANNEL Another advantage of Synchronous Random Pulse Sequences representation, besides inexpensive multiplication as described in Section h, is that an analog quantity represented as an SRPS may be inexpensively and easily gated or multiplexed using an "And" gate. In Trans for matrix each stochastic processor point (there are 102U in all) contains one "And" gate to multiply the input image SPRS and the coefficient SRPS; while the second "And" gate in the same integrated circuit package is used to multiplex the parallel SRPS's representing the input image into a serial signal. 6.1 System Operation The block diagram for the input image display channel is shown in Figure 6.1. The basic timing and gating pulses discussed in Section 3.2 are produced in the clock control and gating control units. Because the oscillo- scope is displaying the intensity of an output point while the next output points intensity is being calculated, a ten bit m-n counter must produce the present m-n position as m and n analog voltages for the vertical and hori- zontal axis of the oscilloscope; and the next m-n position as digital gating commands for multiplexing the SRPS signals. Since each of the 32 stochastic processor cards contains 32 processors or one column of the input picture, the display raster and multiplexing is done vertically to minimize the transients caused by switching between cards. Conventional television uses a horizontal raster. a 05 O H ft w •H Q CD bO ctf a -p ft o •H « o o H pq H CD •H 97 Each stochastic processor card contains a 32 input "NOR" gate, and the outputs from these 32 "NOR" gates drive a 32 input "NAND" gate, Figure 6.1. At this point the intensity (0 to 1) in SRPS form is represented as the fraction of time out of a 32.552 microsecond period that the output of the "NAND" gate is a logical one. This SRPS signal is, thus, digitally integrated by "Anding" it with the ten megahertz system clock and counting the number of pulses produced out of 325 possible time slots. The normalized output intensity (0-1) is now represented by the binary number in the counter divided by 325. The digital integrator, which is driven by a non-retriggerable monostable multivibrator to keep noise spikes from triggering the counter, is composed of two counters. The first counter, which is preset to a binary nine at the beginning of each integrating period, produces an output pulse for every eleven input pulses. The second counter, which is counting the outputs from the first counter, produces a binary number falling between and 30 which represents the quantized gray level of the image to be displayed. At the end of this integration period, while the input to the counters is inhibited, the 5 bits containing the output gray level are gated into a 5 bit storage register and the counters are reset. During the next integration period, the binary number in the storage register is converted to a one out of 30 line representation and then to an analog voltage, which drives the z-axis of an oscilloscope, by one of the following methods. 6.2 Logarithmic Sensation Display (5) From the Weber-Fechner Law S B 98 where S-, and S are the sensations corresponding to the brightness B and B^ respectively. Thus, with the output intensity z represented by one out of 30 lines and the nonlinearity compensated for, the eye gives us the logarithmic trans- fer function required. Mathematically with the brightness a linear function of the calculated output from the storage registers S = log 10 B = K log 10 z (6.2) Since we want to produce a sensation from to 1 which has a logarithmic variation, the brightness is given by B = ^N (6.3) N = 1, 2, 3, . . ., 30 When the transfer function of the Tektronix 602 oscilloscope is approximated 1 piecewise linear curve, Figure 6.2, the inverse of this curve gives the voltage required to make the brightness a linear function. z=4b < b < 1.6 = -^(B-l.6) + .6, 1.6 < B < 4.5 (6.4) = i(B-4.5) + 1.3, 4.5 < B < 10 ram, Figure 6.3, was used to calculate the z axis drive . d the 30 resistors required in the digital to analog ■ ;uit was described in Section h. 3. J 4, to produce the 99 {/) 111 i/) > w z t- H < I -J O Ld or cr Q t/) X < N .. CO • - to ■ ^ .. CM GO CD CM a o •H -P O U q; <+h w c CD ft O o w o rH rH •H O w o OJ o MD X •H G O *n ■P 33 FIK'<1AT ( 1H1 ,T4, ' VI1I.T 2'MD AMP CORR • , T24 , ' Vill. T 1ST AMP CORR', 1 ThS,'I)P AMP INPUT KFS. •♦ TftH, •COMDIICTAIMCF ', T85, ' TOTAL CONDI If. T ANCF 2 • , Tl OH, 'HP AMP CORR • ) 0=1 .0 + 1 000. -07 Our|l+.ni n > = OA/70()Q0. DC = 1 .O+UR '10=1 .0/OC on 30 J=l f 30 '/ = VZ < J ) F = ( 200002 ./200000. )*( \/-. 00015 ) ga=g (j ) GX=GZ-GA FZ= 1000. *GX*. 00132*00-0*. 003- . 0002 F + EZ R7=( 1000.*5.421*DD)/EA-2ft.+100. ;a=i .o/kz GZ = GX + (iA ( I )=(,A 7-100. n (ft, 3 1 »r- ,FA,RA,r,A,r,7. ,no U FflKlAT (ftF20.7) o z ~™ III H to < to u ^ UJ Z V) I H £ O x: > < N U) to lO UJ z H I ce in CD UJ > * s -► ro • • CVJ O in in & rH ft w •H « CD c •H o ■H s X! -P •H M ctf o (L) X! -P ^ O cd > •H Q -d- CD M •H 102 6.3 Linear Sensation Display Using the same constraints as given in Section 6.2, a linear sensation display is to be produced from the binary number z in the storage register. Mathematically the 30 quantized sensations are given by S = ~ N log 10 (ll) (6.5) N = 1, 2, 3, . • ., 30 From equation (6.1), the linear sensations as given above are produced from brightness of B = io s - l (6.6) The nonlinear transfer function of the oscilloscope must also be compensated for as in equation (6.h). A computer program, Figure 6.5, was used to calculate the z axis drive voltages, Figure 6.U, and the 30 resistors required in the digital to analog converter to produce the linear sensation. The operator of the Trans format rix then selects either the loga- rithmic or linear sensation digital to analog converter depending on which type display he desires. 103 /*I0 PS=1203,DEPT=nCS,COOE=HRDWRE,NAMF=MARVFt, /* LlNES = 5O0O,360 = 2.5,RFGinN=12'5K,TYPE = MIX // >£XFC F0RTLKGn,TIME.Gn=(2,5) //FORT. SYS IN 00 * DIMENSION G( "•JO) »VZ (3b) C C LINEAR SENSATION DISPLAY C GZ =0 . WRITE (6*27) 27 FORMAT (1H1,T9, 'LEVFL' ,T27, ' Z AXIS VOL T AGF • , T46 , • OP AMP INPUT RES 1 ' ,T69, •CONO'ICTANCF' ) 00 20 J=l,30 S=( .033333* J )*ALOG10( 11.0) A=10.#*S-1.0 I F ( A-l .6)21,21,22 >. 1 V = ( . 6* A ) / 1 . 6 GO TO 25 22 IF(A-4.5)23,23,24 2 3 V=(.7#(A-1.6))/2.9+.6 GO TO 2 5 ?4 V = ( .7- ( A-4.5 ) ) /'S .5 + 1 .3 ?^ V7(.I) = V RA=lono.*5 .42/V RH=KA+100. GA = 1 ./RR GZ=GZ+GA G(J )=GA 20 WRITE (6,26)A,V,RA,GA 2h FORMAT (4E20.7) 00 10 1=1,5 URI FE( 6,331 33 F0RMAT(1H1,T4, • VOLT 2ND AMP CORR • , T24, ' VOL T 1ST AMP CORR", 1 T'.S.'OP AMP INPUT RES. • ,T68 , 'CONDUCTANCE' ,TH5, 'TOTAL CONOUCTAMCF 2 ' » T 1(18 , » ilP AMP CORR ' ) = 1 .0+1000. *GZ DA = r>+.01 0B=nA/70000. nc=l .o+Oh nn=i .o/oc "ii 30 J = l ,30 V = V Z ( J ) F= (200002./ 2 00000. )*( V-.00015 ) GA=G( .) ) GX=G/-GA F7=1000.*GX#.00132*OD-n*.003-.0002 F A = E + F Z R7.= l 1 000. *5. 421*00) /FA-26.+100. GA=1.0/RZ GZ=GX+GA G(J )=GA RA=RZ-100. 30 WRITE (6,31 )E,EA,RA,GA,r,Z,OD 31 FURMAT ( 6^20.7 ) 10 WHITF (6,32) 32 FORMAT (///) STOP Figure 6.5 Program for Linear Display 104 7- A GENERALIZED TRANS FORMATRIX PROCESSOR 7.1 Resolution The single drawback to the Trans formatrix system is that the resolution of the input and transformed image is only 32 by 32, containing 1024 image points . Since the circuitry required to transform a given image costs about $17.00 per point, one can easily see that a 100 by 100 system with 10,000 points would be about the maximum attainable with today's technology. However, in the future LSI technology may bring the circuitry costs down to a level where a 500 x 500 resolution Trans formatrix is feasible. One method of improving the resolution of the system, while only increasing the cost linearly, would be to increase the number of image points in only one direction, say vertical as in Figure 'J.l. 7.2 Rule Relating Accuracy, Resolution, and Bandwidth When Processing Television Images While trying to increase the resolution of Trans formatrix, not only does the cost of the parallel processors go up but also the intensities in the output display becomes less accurate. In order for the accuracy of the output intensities to remain the same, the frequency of the stochastic processor clock must be increased, making circuit implementation very difficult. The ;ideration of the above problem lead to the following rule and corollary. 105 Figure 7.1 A Picture with Poor Resolution in the Horizontal Direction io6 RULE: Under the two given conditions, the processing rate, of an image processing system, depends only on the maximum image movement rate versus the resolution of the processor (number of parallel processing channels); and not on the television frame rate. GIVEN ; 1. The input to the image processor is from a standard 525 line television receiver. 2. The output of the image processor can be displayed on a variable persistance monitor, or stored in a refresh memory to be actually displayed at regular television frame rates. PROOF: The second half of the rule has already been proven by reference {2h) . Also, many slow scan television systems are in use today which transmit video at less than 30 frames per second. The first half of the rule will be shown by the following example of the Trans formatrix system. From (5), an object moving completely across the screen in less than 5 seconds will not jump or blur. Suppose that the system has a resolution of 32 sensing devices per television line; and a vertical bar is moving across the television screen at its maximum rate. Thus the bar is affecting the output of 5 one sensor for — '— - 156 milliseconds, which is almost ten field times. Since the bar must be sensed only once per processor cycle, the processor may operate at a rate of one-tenth the television frame rate. 1 2 0€ \ t 5 a temporary storage device allowing the image processor's he les e television's frame rate, while still displaying a . picture. 107 COROLLARY: In a stochastic parallel processing machine, the accuracy of the output display is inversely proportional to the information band- width of the image being processed, and inversely proportional to the resolution of the image being processed. Where (Max % Error) = U) X (# sensors /line) [(10) x (S)] 1 / 2 (7.i: _7 GIVEN: 1. The maximum clock rate is 10 megahertz; T = 1 x 10 seconds. 2. The output's accuracy per point is given by equation (4. 11) as % Error) = 200[ p( - 1 " P ^ ) ] 1//2 (7.2) PROOF : 3. Equation (7*2) has a maximum when p = .5. h. The fastest an object can possibly move in the television image is one screen width per S seconds. 5. The pictures to be processed are square. 1. The maximum calculation time allowable per image point is TA S seconds (# sensors) (7.3: 2. The total number of time slots available per image point is n = TA T 2 -7 (# sensors per horizontal line) x 10 (7.*0 (7.5) 108 3. The maximum % Error is given by: (Max. < z UJ a: u z a: H _ _i it < z ^ — 1/) u I/) »- z U. < 3 UJ 0. I/) If) CO (E QL o o •H »- h- -P ( ) u ^ < < H u. u. O z z (1J H (- 2 5 2 _l _l > I/) i/i >> UJ Q o H UJ ^ < UJ or 0. o 1/1 o or H- CD o -p n u. 1 < O i CD H OJ • 0) •H 110 8. CONCLUSIONS In order to show that the circuitry to be used in Trans formatrix was practical, a h x k model of Transformatrix, called "Model T", Figure 8.1, was built. A description of "Model T" is given in (25). Both "Model T" and Trans formatrix may be seen at the Circuits Research Group, Department of Computer Science, University of Illinois, Urbana, Illinois, at any time. This thesis has described the theoretical considerations "systems design" and special circuits required in order to build Trans formatrix. It has shown that inexpensive computing elements can be used in the worlds most highly parallel processor to transform visual images. In fact, Transformatrix stands alone as the only machine which can perform the two-dimensional Fourier Transform at television frame rates. Ill Figure 8.1 Picture of "Model T" 112 APPENDIX 113 Al. TWO DIMENSIONAL FOURIER TRANSFORM PROGRAM Al.l Program Description A computer program, which simulates the Fourier Transform mode of Transformatrix, was written. This program processes input pictures with a resolution of 32 by 32 and 10 gray levels. Many interesting examples were derived from this program in order to demonstrate the ability of Transformatrix to perform the Fourier Transform. The program listing is shown in Figures A.l and A. 2. A1.2 Examples Each simulation of the Fourier Transform displays the input image; real part; imaginary part; and magnitude of the Fourier Transform. Six examples are given here. (A) Figure A- 3 shows four rows and four columns with a brightness of 10 and two blank spaces between each row and column. (B) Figure A-k shows the same pattern as Figure A- 3 but displaced within the input picture. (C) Figure A- 5 shows four rows and four columns with a brightness of 10 and four blank spaces between each row and column. (D) Figure A-6 shows the same pattern as Figure A- 5 but with decreasing intensities (10, 8, 6, h) . (E) Figure A-7 shows diagonal lines of brightness 10 with two blank spaces between each diagonal line. (F) Figure A-8 shows an application to number theory where (1) f (x,y) =10 if x and y are relative prime (2) f (x,y) =0 if x and y have a common divisor greater than one. Dl MEN SUN X ( 32, 32 ), YA( 32,32), YB( 32, 32),Y C( 32,32) ,C( 33) ,ZCt 3), nl+ 1 MZ(3) FOURIER TRANSFORM oU REAU( Si 16)KA ,Kb, ia,KO,KE,KF,KO,KH,NA,NB,^: , ND,NE,NF,NG,NH 16 FORMAT (1613) INTEGER YA,Yd, YC ,x UU 5 J=l, 32 OU -j 1=1,32 b X( I, J)=0.0 JU lb J =1,32 X( NA, J) = KA X ( tM L> , J )=Kl) X( NC, J)=KC X(NJ ,J )=KJ X( J,Nfc)=KE X{J ,NF )=KF X( J,,^o)=KG 15 X (J ,HH )=KH L< l)=l.O JU 17 J=2,9 r> = 6.283i8b3/ 32 M=J-1 .0 17 L( J)=CQS( P*M) JU Id J=2,9 V=l J-J N=J-1 Id L(M)=-C( N) JU 1^ J=2,9 f=2/-J vi = 7«-J 1 i lM) = C( N) JU ^0 J=2,^ N=33-J N=J-l 2U U M) = C( N) 00 23 L = l, 32 IK L-16) 66, 86, H7 oo LZ=l7-l GO TJ 63 67 LZ=49-L oo LA=L-l JU , 3b, ,71 n KA^l A*JA*KA* IA Figure A.l Fourier Transform Program 11 IH MA-32)2 7,2 7,21 21 MA=MA-32 GO TO 22 27 ^e=MA+8 Zi IF M0-J2 )24,2 CCNTlNUt *RITL (o,4U) 40 FORMAT CIS//////////////////////////////////////////////////// I ///////////, T59,'IMPUT PICTURE') *KI Tt( 6,41 )X 41 FURMAT(32l 4/ > ^KITE (6,42) <♦= - v - a o o a a - ■ ■ ■■ , o n o o t ■eQao/*oa9o^n9oa«« Taooooa-ia^a^ao'S - 3 o . o - - o -> o t o o o n e - - o^o^oO©©- » - ^ , ■ o a o « — — a a "^ '-> *oaaoaaaoae "» a a a a -i aaa»->aooaeoeaoe->f»aaaoaaooaoOaOo "* *' 1 *'*'^©a-»*»o-»o-»«o.-»o oaar-e^ettaA^anoo oooaooOo^-so^-iao-. 1 ^ ■ I — - -> a ■> 3 *1 n -^ O a -• — ^-,13-5-3-t-*-. ■»—->■>-> 0"^T*-> — — O -> T -1 J 3 ° - T Figure A. k Example 2 of the Fourier Transform 118 Fig'> f the Fourier Transform 119 Figure A. 6 Example k of the Fourier Transform 120 <•»••• ; s • - t Figure A. 7 Example 5 of the Fourier Transform 121 °»2ss»;s Figure A. 8 Example 6 of the Fourier Transform 122 LIST OF REFERENCES 1. Poppelbaum, ¥. J., "Projects in the Hardware Research Group of the Department of Computer Science of the University of Illinois", Department of Computer Science Report #238, University of Illinois, Urbana, Illinois, April, 1968. 2. Ait, Franz L. , Rubinoff, Morris, Advances in Computers - Volume j , Academic Press, 19&9* 3. Ryan, L. D., "Circuit and System Design of the Trans formatrix Processor", Department of Computer Science Report (to be published), University of Illinois, Urbana, Illinois. k. Marvel, 0. E., "Quarterly Technical Progress Report", Department of Computer Science, University of Illinois, Urbana, Illinois, July - September, 1969' 5. Anos, S. W. , and Birkenshaw, D. C, Television Engineering Principles and Practices , Iliffe and Sons LTD, 1953. 6. Afuso, C, "Analog Computation with Random-Pulse Sequences", Department of Computer Science Report #255 3 University of Illinois, Urbana, Illinois, February, 1968. 7. Esch, J., "Rascel - A Programmable Analog Computer Based on a Regular Array of Stochastic Computing Element Logic", Department of Computer Science Report #332, University of Illinois, Urbana, Illinois, June, I969. 8. Poppelbaum, W. J., Afuso, C. and Esch, J. W. , "Stochastic Computing Elements and Systems", AFIPS Proceedings, 1967 FJCC, Vol. 31, pp. 635-644. y. Marvel, 0. E., "Quarterly Technical Progress Report", Department of Computer Science, University of Illinois, Urbana, Illinois, October - December, 1967. 10. Peterson, W. W. , Error-Correcting Codes , MIT Press, 1968. 11. .., G. A., Random Process Simulation and Measurement , McGraw-Hill Book C ompany, Inc., 1^66. . Martin, A. J., "PRBS Can Fool the System", Electronics , April 28, 1969- . , "System Identification by Means of Pseudo-Random Binary Pulse Sequences", Electronic Instrument Digest , November, 1969* .. "] ndom Numbers Generated by Linear Recurrence Modulo Computation , April, I965. 123 15 . Knuth , D . E . , The Art of Computer Programming - Volume 2 Semi numerical Alogrithms , Addis on -Wesley Publishing Company, 1969* 16. Anderson, G. C, Finnie, B. W. , and Roberts, G. T. , "Pseudo Random and Random Test Signals", Hewlett-Packard Journal , September, 1967. 17. Koo, Tuh Kai, "Opto-Electronics Switching Matrix", Department of Computer Science Report #270, University of Illinois, Urbana, Illinois, May 1968. 18. Shockley, W. , and Read, W. T., Physics Review , 87, 1952. . Hall, R. N., Physics Review , 87, 1952. 20. Buhl, R. H. , Photoconductivity of Solids , John Wiley and Sons, New York, I960. 21. Bauer, Georg, Measurement of Optical Radiation , Focal Press, 1962. 22. Larach, Simon, Photoelectronic Materials and Devices , D. Van Nostrand C omp any , Inc . , 1965 • 23. Schwara, Ralph and Friedland, Bernard, Linear Systems , McGraw-Hill, Inc. 1965. 2*4-. Rollenhagen, D. C, "The Vista System for Compression of Television Signal Bandwidths", Department of Computer Science Report #35^-? University of Illinois, Urbana, Illinois, October, 1969» 25. Marvel, 0. E., "'Model T' A Demonstration of Image Multiplication Using Stochastic Sequences", Department of Computer Science Report #3^-9 > University of Illinois, Urbana, Illinois, August, 1969* 124 VITA Or in Edward Marvel was born in White Plains, New York, on September 23, 19^0. He graduated from Ft. Lauderdale High School, Ft. Lauderdale, Florida in 1958. In 1963 he received his B.S. Co-Op in Electrical Engineering from the Georgia Institute of Technology having completed seven work quarters at Martin-Marietta, Orlando, Florida. While teaching half time, he received his Masters in Electrical Engineering from Georgia Institute of Technology in 1965. After graduating number one in his class from the United States Army Ordnance Guided Missile School, he was stationed at White Sands Missile Range, New Mexico. After two and a half years with the Radar Division of White Sands Missile Range, he was released from active duty a captain and awarded the Army Commendation Medal for his work with the FPS-16 radars and ARCADE computer system. In 1^*67 he joined the Circuit Research Group, under Dr. Poppelbaum, to work toward a Ph.D. in Electrical Engineering. He is a member of Tau Beta Pi, Eta Kappa Nu, Chi Gamma Iota and the IEEE. Form AEC-427 (6/68) AECM 3201 U.S. ATOMIC ENERGY COMMISSION UNIVERSITY-TYPE CONTRACTOR'S RECOMMENDATION FOR DISPOSITION OF SCIENTIFIC AND TECHNICAL DOCUMENT ( See Instructions on Reverse Side ) 1. AEC REPORT NO. COO-li+69-Ol6l 2. TITLE TRANSFORMATRIX - AN IMAGE PROCESSOR - INPUT AMD STOCHASTIC PROCESSOR SECTIONS 3. TYPE OF DOCUMENT (Check one): (X) a. Scientific and technical report I I b. Conference paper not to be published in a journal: Title of conference Date of conference Exact location of conference Sponsoring organization □ c. Other (Specify) 4. RECOMMENDED ANNOUNCEMENT AND DISTRIBUTION (Check one): KM a. AEC's normal announcement and distribution procedures may be followed. I I b. Make available only within AEC and to AEC contractors and other U.S. Government agencies and their contractors. "2 c. Make no announcement or distrubution. 5. REASON FOR RECOMMENDED RESTRICTIONS: 6. SUBMITTED BY: NAME AND POSITION (Please print or type) Or in E. Marvel Research Assistant Organization Department of Computer Science University of Illinois Urbana, Illinois 6l801 Signature L^/U-y^ £ • sm-tu^m-J I '*>: