COMPUTER SYSTEM FOR PRODUCING VARIOUS FOURIER ANALYSES IN REAL TIME

• US 3,586,843 A
• Filed: 12/26/1968
• Issued: 06/22/1971
• Est. Priority Date: 12/26/1968
• Status: Expired due to Term

• Current Assignee: Edwin A. Sloane
• Original Assignee: Edwin A. Sloane
• Inventors: Sloane, Edwin A.
• Application Number:
  US04/786,869
• Time in Patent Office: 908 Days
• US Class Current: 708/5
• CPC Class Codes: F02B 2075/027 four
• CPC Class Codes: G06J 1/00 Hybrid computing arrangements digitally-programmed analogue computers G06G7/06

Abstract

A computer for realizing Fourier transformations utilizing the mathematical realization that the Fourier transform can be synthesized by a sampling technique, wherein any sample of a time function can be described in the frequency or complex frequency domain by, for example, a sine and cosine function having a periodicity with respect to frequency that is proportional to the displacement of the sample from a selected time zero, multiplied by an amplitude proportional to the magnitude of the respective sample. In the basic embodiment the apparatus elements provide for the summation of the products of the sample amplitude and the appropriate sine and cosine function, whereby a continuous up-todate Fourier transformation is available for all of the sampled time functions presented to the computer at any point in time.

Claims

1. A computer for deriving a Fourier transform from an input signal during a selected input signal duration, the combination comprising:

control means for generating an interrelated plurality of series of clock pulses;

means for generating signals representing successive increments of a function, wherein the function is defined as having a characteristic which changes with each increment relative to the passage of computing time, and a new iNcrement is generated in response to each clock pulse of a selected one of the series of clock pulses applied thereto;

sample and hold means for sampling the input signal at selected sampling intervals during the input signal duration to provide a sampled signal at said selected sampling intervals and for generating an output signal representative of the amplitude of said sampled signal, wherein the increments of said incrementally varying function have a predetermined value for each successive one of said sampling intervals;

input means for introducing said input signal to said sample and hold means;

multiplier means coupled to said means for generating and to said sample and hold means for multiplying selected increments of the function by respective sampled signals to derive product signals;

storage means operatively coupled to the multiplier means for storing the product signals derived by said multiplier means;

wherein said control means is operatively coupled to said sample and hold means, to said means for generating, and to said storage means to provide to each of the means a respective series of clock pulses;

wherein the sample and hold means samples the input signal at the start of each sampling interval in response to its respective clock pulses, the means for generating a function generates a successive increment during each sampling interval in response to its respective clock pulses, and said multiplier means effects said multiplying of the function increments by the sampled input signals and introduces the resulting product signals to the storage means, said control means including means to access the storage means in response to its respective series of clock pulses to store the products in the storage means, said storage means providing an up-to-date Fourier transformation in real time for the input signal introduced to the sample and hold means; and

means associated with the storage means for utilizing the up-todate Fourier transformation in real time.

2. The computer of claim 1 wherein the Fourier transform is derived from a time limited, bandwidth limited, time function input signal, wherein the means for generating includes elements which cooperate to provide a trigonometric function with a frequency which varies incrementally with the passage of time, wherein a different predetermined frequency is generated during each successive sampling interval;

said multiplier means including elements to multiply the successive signals corresponding to the frequencies of the trigonometric function by the respective sampled signals and introduces the product signals thereof to said storage means.

3. The computer of claim 2 wherein said means for generating further includes elements for generating sine and cosine function signals that have a frequency which varies incrementally from sample interval to sample interval, said frequency varying in proportion to its position in time from an arbitrarily selected time zero position, wherein the multiplier means further includes elements for successively multiplying the sine function signal by the sampled signal and the cosine function signal by the sampled signal and introduces the product signals thereof to said storage means for storage therein as a Fourier transform in response to said means for accessing the storage means.

4. The computer of claim 3 wherein said time zero is defined as the midpoint of said selected input signal duration, and the elements of said means for generating first generate incrementally decreasing frequencies, then zero frequency, and then generate incrementally increasing frequencies.

5. The computer of claim 4 wherein one of the series of clock pulses comprises a sign signal, and wherein the elements of said means for generating include inverter means defining a part of said control means for inverting the phase of said generated sine function in response to said sign signal for times less than time zero to enable said means for generating to generate the incrementally decreasing, zero and increasing frequencies.

6. The computer of claim 5 wherein the elements of said multiplier means are adapted to multiplex said sine and cosine function signals by said sampled signals to provide sine-sample products and cosine-sample products respectively said storage means stores the sine-sample and cosine-sample products in separate storage sections in response to the means to access the storage means, and adder means integral with the storage means and coupled to the multiplier means for adding the values stored in said separate storage sections to the subsequent sine-sample and cosine-sample products respectively received from the multiplier means in response to the means to access.

7. The computer of claim 3 wherein said input signal is an analog signal, said means for multiplying is an analog multiplier means, and includes means for converting the analog multiplier means product output into a digital output, and said storage means is a digital memory means.

8. The computer of claim 7 wherein the storage means includes digital adder means coupled to the means for converting and responsive to the control means for adding the value stored in said digital memory means from a previous multiplication to the succeeding product output of said analog multiplier means, said digital adder means defining a part of said digital memory means to define a coherent memory.

9. The computer of claim 3 wherein said elements of said means for generating further comprises:

plurality of signal generator means for generating a sinusoidal waveform output signal, the frequency of said output signals from each of said signal generator means being different and a multiple of the lowest frequency output from one of said signal generator means;

frequency adder means coupled to the signal generator means for adding the output signals of the signal generator means;

switch means for selectively coupling said frequency signal generator means to said frequency adder means; and

wherein the control means includes control logic means integral therewith for generating a binary code for selectively enabling said switch means to couple said frequency adder means to a predetermined plurality of signal generator means to define an output signal from the means for generating that is the sum of the frequencies generated by the plurality of signal generator means.

10. The computer of claim 3 wherein said input signal defines a frequency function, said sample and hold means includes elements for sampling the input signal at given sample intervals to generate an output signal representative of the frequency of the sampled function, and said means for generating sine and cosine function signals is further adapted to provide a waveform of selected phase shift.

11. The computer of claim 3 including first and second sample and hold means for receiving real and imaginary inputs respectively of a complex time function, wherein said multiplier means includes a first pair of multipliers which respectively receive the sine and cosine function signals and a second pair of multipliers which respectively receive the cosine and sine function signals introduced to the pairs of multipliers by the means for generating said function signals, and second adder means operatively coupled to the two pair of multipliers for providing output signals which define the real and imaginary components of the transformed complex time function, said components being introduced to the storage means to define a Fourier transform of the complex time function.

12. The computer of claim 3 wherein said control means further comprises:

master clock means for generating a train of clock pulses;

counter and decode means coupled to the master clock means for scanning the storage means and the adder means to access same through a selected number of scans, and to determine the frequencies and duration of the predetermined frequencies generated by the means for generating;

preset counter means coupled between said counter and decode means and said means for generating to provide a binary code to the latter in response to the master clock means to select said predetermined frequencies during successive sampling intervals.