CONTINUOUSLY UPDATING FOURIER COEFFICIENTS EVERY SAMPLING INTERVAL

• US 3,778,606 A
• Filed: 02/23/1972
• Issued: 12/11/1973
• Est. Priority Date: 02/23/1972
• Status: Expired due to Term

• Current Assignee: Donald L. Starkey, Joseph W. Schmitt
• Original Assignee: Donald L. Starkey, Joseph W. Schmitt
• Inventors: Schmitt, Joseph W., Starkey, Donald L.
• Primary Examiner(s): Gruber, Felix D.
• Assistant Examiner(s): Malzahn, David H.
• Application Number:
  US05/228,545
• Time in Patent Office: 657 Days
• Field of Search: 235/156,181 324/77B,77G,77H
• US Class Current: 708/403
• CPC Class Codes: G06F 17/141 Discrete Fourier transforms

Abstract

A method and apparatus for continually producing updated Fourier coefficient values of an input signal during each sample time. The Fourier coefficient F(k Omega ) is first calculated for any sequence of N samples of the input signal f(zT). To calculate the Fourier coefficients for the next ensuing sample time, the previously calculated Fourier coefficient value is updated by the addition of the product of the reference value and the difference between the new sample and the sample which occurred N samples earlier in time. This process is continued for each new sample.

Claims

1. Discrete Fourier transform apparatus comprising means for providing a stream of signal samples f(zT), where T is the sampling interval in the time domain and - infinity <

OR = z <

OR = infinity ;

storage means for delaying said f(zT) signal samples for an interval NT, where N is the number of signal samples in the integration interval of the discrete Fourier transform of any sequence f(nT) of said f(zT) samples, where z <

OR = n <

OR = z + N-1;

arithmetic means coupled to receive said signal samples f(zT) and the delayed version thereof and arranged 1. for taking the differences between samples which are NT apart in time so as to provide a sequence of difference values; and

2. for multiplying said sequence of difference values by a sequence of complex reference values R(k Omega zT) for at least one value of k to produce a resulting sequence of products; and

means for accumulating said products to provide an updated Fourier coefficient value for each value of z.

2. for multiplying said sequence of difference values by a sequence of complex reference values R(k Omega zT) for at least one value of k to produce a resulting sequence of products;

and means for accumulating said products to provide an updated Fourier coefficient value for each value of z.

3. The invention as set forth in claim 2 wherein said second network includes a first circuit for multiplying said difference values by the real part of the complex reference signal R(k Omega zT) to produce a resultant sequence of real products and a second circuit for multiplying said difference values by the imaginary part of the reference signal to produce a resulting sequence of imaginary products;

and wherein said accumulating means includes first and second accumulators for accumulating said real and imaginary products, respectively.

4. The invention as set forth in claim 2 wherein said f(zT) signal includes a real part A(zT) and an imaginary part jB(zT);

wherein said storage means includes first and second storage devices for delaying said A(zT) and jB(zT) signal parts, respectively, for the interval NT;

wherein said first network includes first and second circuits for taking the differences between the real and imaginary sample parts respectively, which are NT apart in time so as to produce a sequence of real and a sequence of imaginary values;

wherein said second network includes first and second complex multiplying circuits for multiplying said real and imaginary difference value sequences by the complex reference signal to produce a sequence of real and a sequence of imaginary products; and

wherein said accumulating means includes first and second accumulators for accumulating said real and imaginary products, respectively.