Electronic transform system

An electronic system providing discrete mathematical transforms includes a charge-coupled transversal filter, a pair of sample and hold circuits connected to the output of the filter, and a differential amplifier connected to the outputs of the pair of sample and hold circuits. An analog-to-digital converter is connected to the output of the differential amplifier. A transmitter of intelligence is connected to the output of the analog-to-digital converter for sending compressed intelligence via a data link.

BACKGROUND OF THE INVENTION 
This invention is in the field of mathematical transform mechanization, and 
particularly in the area of mechanization of direct and inverse Hadamard, 
cosine and sine transforms. 
No prior art appears to exist wherein the mechanization is provided by 
utilizing charge-coupled transversal filters, pairs of sample and hold 
circuits and differential amplifiers processing the outputs of the sample 
and hold circuits. 
SUMMARY OF THE INVENTION 
An electronic system for providing discrete mathematical transforms, 
comprises the combination of a charge-coupled transversal filter, a pair 
of sample and hold circuits connected to the output of the filter, and a 
differential amplifier connected to the outputs of the pair of sample and 
hold circuits. 
An analog-to-digital converter is connected to the output of the 
differential amplifier. A transmitter of digital intelligence is connected 
to the output of the analog-to-digital converter. A receiver may be 
electromagnetically coupled to the transmitter via a data link. A 
digital-ao-analog converter may be connected to the output of the 
receiver. Means connected to the output of the digital-to-analog converter 
are provided for converting a direct transform of intelligence as a 
function of time. 
The invention may be alternatively described as a method for electronically 
providing discrete mathematical transforms, by generating a signal 
comprising a carrier modulated by intelligence, sampling the generated 
signal and providing at least one set of summed intelligence components, 
selecting a predetermined portion of each of said at least one set of 
summed intelligence, and sensing the difference between two selected 
portions of each of said at least one set of summed intelligence. 
Additionally, functions performed include switching said difference so that 
each portion of said at least one set of summed intelligence is provided 
in serial outputs, and transforming the serial outputs into the time 
domain thereby providing the inverse transforms of said at least one set 
of summed intelligence. 
Such invention provides a direct Hadamard transform. Also provided by the 
same equipment is a direct cosine transform and/or a direct sine 
transform, as well as inverse transforms thereof.

DETAILED DESCRIPTION 
Referring to the drawings, Hadamard transform system 10 is mechanized in 
FIG. 1, utilizing charge-coupled circuits. This system has the capability 
of not only converting an amplitude modulated carrier having intelligence 
components therein, but also providing the inverse transforms by utilizing 
another transform system 10 in series with a first transform system to 
restore the intelligence to the time domain as inputted at 11. 
Hence output from a data source, such as a video camera, can provide AM 
modulated series of pulses at 11, a typical one-half of a modulation 
envelope being shown in FIG. 2 at A, showing a carrier contour of the 
pulse intelligence therein. 
The modulation envelope is fed to a plurality of CCD transversal filters 
20, which in this example takes 16 samples of the analog AM data at B, as 
illustrated by FIG. 3. The numerical values shown on curve B illustrates 
the typical relative amplitudes of each of the 16 samples taken. 
Therefore, each filter 20 receives all the 16 samples in their time 
sequenced order as shown in FIG. 3. Filter 20 comprises a shift register 
type structure, so that the first of the 16 samples is registered in a 
first location in the filter. When the second sample comes along, it 
shifts the first sample to a second position of the register, the second 
sample being registered in the first location. This process continues 
until all 16 samples are loaded in the register. Then, at a subsequent 
time period following the loading of the 16 samples, all such samples are 
fed into the sample and hold circuits simultaneously and in parallel as 
below described. 
CCD transversal filters are known in the art, examples of which may be 
found in the textbook entitled Charge Transfer Devices by Sequin and 
Tompsett, pages 216-231, copyright 1975, published by Academic Press, New 
York. 
Although only two channels, duplicate of each other, are illustrated, it is 
to be understood that multiple channels are required, each to handle one 
Hadamard coefficient. 
Each of filters 20 will have + and -bus outputs that connect each filter to 
a sample and hold circuit 30. The filter which provides the lowest order 
Hadamard coefficient of the transformation, denoted by sequency zero, has 
all its taps, in this case 16 taps for each of the 16 samples taken, 
connected to the +bus. Hence, the transform coefficient resulting 
represents the sum of all samples and corresponds to the DC level of all 
samples or average value of the 16 analog samples. All other filters, 
representing sequencies 1-15, have 8 taps or outputs from filters 20 
connected to the +bus and 8 taps or outputs connected to the -bus. The 
order of output connections from filter 20 is dependent on the particular 
sequency processed. 
Sample and hold circuits 30 are known in the art and may be found in a 
textbook entitled Mossfet in Circuit Design by Crawford, pages 108-109, 
published by McGraw-Hill, New York, Copyright 1967. 
Thus, the + and -bus inputs to each of a respective sample and hold circuit 
30, results in the sampled data as at B to be fed to and again sampled by 
circuits 30 which feed their output samples into a differential amplifier 
40, which amplifier 40 takes the difference between the samples from each 
of the circuit 30 pair outputs, and provides a Hadamard transform 
coefficient in a pulse output form, the amplitude of which varies in 
accordance with the difference between the + and -bus bar outputs. These 
coefficients are designated as M.sub.1 . . . M.sub.16 representing 16 
sequencies of the direct Hadamard transform. 
Such Hadamard coefficients, of differing pulse amplitudes, are fed into a 
CCD parallel to serial converter for enabling the coefficients in terms of 
M.sub.1 . . . M.sub.16 to be passed therethrough in the order in which the 
input intelligence at A appears at 11. 
The complete direct Hadamard transform will therefore appear at 51 at the 
output of converter 50. 
Such complete Hadamard transform is reflected by and represented in its 
mathematical matrix counterpart as shown in FIG. 4, wherein the direct 
Hadamard transform is defined as: 
EQU F(u) = H .times. f(t) 
wherein H is the Hadamard matrix represented by + and - symbols which 
indicate +1 and -1 logic levels, f(t) matrix represent the relative 
amplitudes of the 16 samples of analog data as at B in FIG. 3. M.sub.1 . . 
. M.sub.16 is a matrix representing the Hadamard coefficients available as 
inputs into converter 50 to provide Hadamard sequencies 0, 1, . . . 15 at 
51 representing the complete direct Hadamard transform of the particular 
case illustrated in in FIG. 4. 
The complete matrix multiplication is arrived at by multiplying the first 
element in the first row of H by the first element in f(t) which is 48. 
Then the second element of the first row of H is multiplied by the second 
element in f(t) which is 50 and so on until all elements in the first row 
of H have been multiplied by the elements in f(t). These resultant 
products are algebraically summed to provide the first Hadamard 
coefficient M.sub.1 which is +466. The process is repeated with the second 
row et seq. of H multiplied by f(t) to obtain the second Hadamard 
coefficient -112. This process is repeated until all rows of H have been 
multiplied by f(t) and all Hadamard coefficients are computed. 
It is noted that CCD parallel to serial converter at 50 may be found in the 
same textbook above mentioned entitled Charge Transfer Devices at pages 
207-209. Though showing a CCD converter at 50, a conventional parallel to 
serial electronic converter may be used. 
It should also be noted that differential amplifier 40 is known in the art 
and may be found in the textbook entitled MOS/LSI Design and Application, 
by Carr and Mize, pages 291-293, published by McGraw-Hill, New York, 
copyright 1972. 
To obtain transformation of the 16 Hadamard sequencies back to the time 
domain which is the inverse transform, another system as at 10 may be used 
being connected to output 51. The output of the second system 10 at 52 
will provide the inverse transformation of the intelligence received from 
the original data source at 11 to intelligence components shown in curve B 
as a function of time. 
The circuit above may be utilized in a data transmission link to rapidly 
send data which has been compressed by Hadamard transformation to a 
receiver and then reconverted to original intelligence as a function of 
time. 
Such system therefore may employ an analog-to-digital converter at 60 
connected to each of the plurality of outputs from differential amplifiers 
40 which converts the analog parallel inputs to serial digital signals. 
The digital outputs from converter 40 are fed into a transmitter 70 
capable of transmitting modulated intelligence in digital format, to 
enable the compressed data to be fed into either a land line or 
electromagnetic radiation data link at 75 which link is coupled to a 
receiver that demodulates the carrier signal and passes the intelligence 
signals of the digital pulse information to a digital-to-analog converter 
90. Converter 90 changes the digital data into analog information which 
may then be fed into system 10 to provide the Hadamard sequencies via such 
communication link as at B. 
Each differential amplifier output at 41 provides an individual Hadamard 
coefficient which is part of the direct Hadamard transform. Hence, at 41 
the Hadamard coefficients are provided in parallel, one from each 
differential amplifier output, as inputs to the parallel to serial 
converter 50. Therefore at 51, the output of converter 50, there will be 
provided the Hadamard coefficients in serial format and in predetermined 
sequence. 
Accordingly, by passing the serially formatted Hadamard coefficients 
through a like subsystem 10, the analog curve B is re-established at 52, 
at the output of the second subsystem 10. 
The branch consisting of circuits 60, 70, 80, 90 and 10, is fed by 
differential amplifiers 40 thereby providing such branch the same Hadamard 
coefficients at 41 as inputs to analog-to-digital converter 60. Hence, the 
Hadamard coefficients at 61 are in digital format feeding transmitter 70, 
as above discussed. Hence, after processing the received signals by 
receiver 80, the Hadamard coefficients in digital form are fed into a like 
subsystem 10 to reconvert from direct transform format to inverse Hadamard 
transform format to likewise reconstruct the analog sampled data as at B. 
The discussion above related to mechanization of a Hadamard transform and 
its inverse transform. It is pointed out though that intelligence in 
either cosine transform of sine transform can be processed by the same 
equipment detailed in FIG. 1 in similar manner as described in connection 
therewith for the Hadamard transform and its inverse transform to 
reconvert same to the time domain.