Serial-access linear transform
First Claim
1. A serial-access linear transform apparatus, suitable for signal processing systems requiring the rapid generation of linear transforms of a spatial or temporal signal, where the transform is in sampled form consisting of a series of N-sample terms, and where the signal consists of a series of N-sample pulses, comprising:
- a data source, for providing the signal which is to be processed into a linear transform, the output of the data source being the function g(t);
a first function generator, which generates a function a(t);
an input multiplier, whose two inputs are the outputs, g(t) and a(t), of the data source and the first function generator, for multiplying the two inputs, the output of the multiplier being a(t)g(t);
a linear filter having an impulse response b(t), whose input is the output signal, a(t)g(t), of the input multiplier and whose output is the signal integral a(u)g(u) b(- u) du;
a second function generator, which generates the function c(t);
an output multiplier, whose inputs are the outputs of the linear filter and of the second function generator, and whose output is the desired sequence of terms of the linear transform, namely integral (a(u)b(t-u)c(t))g(u) du.
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Abstract
A serial-access linear transform device, suitable for signal processing systems requiring the rapid generation of linear transforms of a spatial or temporal signal, where the transform is in sampled form consisting of a series of N-sample terms, each term consisting of factors, and where the signal consists of a series of N-sample pulses. The transform device includes a time code generator which generates a plurality of pulses, either singly or sequentially, at predetermined intervals of time, and serves as a clocking and synchronizing source for the transform device, and a data source for providing the signal which is to be processed into the form of a linear transform. A first read-only N-sample memory is synchronized by the timecode generator, the memory containing information regarding one of the factors of the series of N-sample terms of the linear transform. A first multiplier, whose two inputs are the outputs of the data source and the first read-only memory, multiplies the two inputs. A second read-only N-sample memory is synchronized by the timecode generator, this memory also containing information regarding factors of the series of N-sample terms of the linear transform. A cross-correlator may comprise: (1) a first N-sample shift register, whose input is the output of the first multiplier, which provides a useful output when the N stages are filled; (2) a second shift register, substantially identical to and synchronized with the first shift register, having as its input the output of the second read-only memory; (3) a plurality of N shift-register (S-R) multipliers connected between corresponding stages of the two shift registers, the totality of S-R multipliers serving to cross-correlate the contents of the two shift registers; and (4) a signal summer, whose inputs are the outputs of the N S-R multipliers, having as its output a sequence of terms each of which is a factor of the final sequence of terms in the linear transform. A third read-only memory, substantially similar to the first and second read-only memories, stores the final necessary factors for the sequence of terms in the linear transform. A second multiplier, whose inputs are the outputs of the signal summer and of the third read-only memory, has as its output the desired sequence of terms of the linear transform.
52 Citations
6 Claims
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1. A serial-access linear transform apparatus, suitable for signal processing systems requiring the rapid generation of linear transforms of a spatial or temporal signal, where the transform is in sampled form consisting of a series of N-sample terms, and where the signal consists of a series of N-sample pulses, comprising:
- a data source, for providing the signal which is to be processed into a linear transform, the output of the data source being the function g(t);
a first function generator, which generates a function a(t);
an input multiplier, whose two inputs are the outputs, g(t) and a(t), of the data source and the first function generator, for multiplying the two inputs, the output of the multiplier being a(t)g(t);
a linear filter having an impulse response b(t), whose input is the output signal, a(t)g(t), of the input multiplier and whose output is the signal integral a(u)g(u) b(- u) du;
a second function generator, which generates the function c(t);
an output multiplier, whose inputs are the outputs of the linear filter and of the second function generator, and whose output is the desired sequence of terms of the linear transform, namely integral (a(u)b(t-u)c(t))g(u) du.
- a data source, for providing the signal which is to be processed into a linear transform, the output of the data source being the function g(t);
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2. The transform apparatus according to claim 1, wherein the function a(t), generated by the first function generator, corresponds to the sequence W0, W0.5, . . . , W0.5(N 1) , where W e i2 /N;
- the function c(t) corresponds to the same sequence; and
the linear filter has discrete impulse response e i n /N, for n -(N-
1), . . . , (N-1).
- the function c(t) corresponds to the same sequence; and
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3. The transform according to claim 2, wherein the linear filter is an acoustic surface wave device;
- and the function generators are serial-access memories.
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4. A serial-access transform apparatus, suitable for signal processing systems requiring the rapid generation. of linear transforms of a spatial or temporal signal, where the transform is in sampled form consisting of a series of N-sample terms, each term consisting of factors, and where the signal consists of a series of N-sample pulses, comprising:
- a time code generator which generates a plurality of pulses, either singly or sequentially, at predetermined intervals of time, and serves as a clocking and synchronizing source for the transform apparatus;
an initializing signal source, whose output is connected to the time-code generator, which generates pulses which control timing signals for the generation of a complete set of operating cycles of the transform;
a data source, for accepting the signal which is to be processed into the form of a linear transform;
a first read-only N-sample memory, synchronized by the timecode generator, the memory containing information regarding one of the factors of the series of N-sample terms of of the linear transform;
a first input multiplier, whose two inputs are the outputs of the data source and the first read-only memory, for multiplying the two inputs;
a second read-only (2N-1)-sample memory, synchronized by the time-code generator, this memory also containing information regarding factors of the series of N-sample terms of the linear traNsform;
a cross-correlator comprising;
a first N-sample shift register, whose input is the output of the input multiplier, and which provides a useful output when the N stages are filled;
a second shift register, substantially identical to and synchronized with the first shift register, whose input is the output of the second read-only memory;
a plurality of N shift-register (S-R) multipliers, connected between corresponding stages of the two shift registers, the totality of S-R multipliers serving to cross-correlate the contents of the two shift registers;
a signal summer, whose inputs are the outputs of the N S-R multipliers, and whose output is a sequence of terms each of which is a factor of the final sequence of terms in the linear transform;
a third read-only memory, substantially similar to the first and second read-only memories, which stores the final necessary factors for the sequence of terms in the linear transform;
a second output multiplier, whose inputs are the outputs of the signal summer and of the third read-only memory, and whose output is the desired sequence of terms of the linear transform.
- a time code generator which generates a plurality of pulses, either singly or sequentially, at predetermined intervals of time, and serves as a clocking and synchronizing source for the transform apparatus;
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5. The transform apparatus according to claim 4, wherein the cross-correlator is an acoustic surface-wave correlator with time-serial input and output at data rates compatible with the data rates of the two multipliers and the three read-only memories.
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6. The transform apparatus according to claim 4, wherein the cross-correlator is a complex cross-correlator.
Specification