Fast discrete transform generator and digital filter using same

Details Fast discrete transform generator and digital filter using same Fast discrete transform generator and digital filter using same

1977-03-18

1978-06-06

Malzahn, David H.

Boots, shoes, and leggings

364724, 364725, G06F 1534

Patent

active

040939944

ABSTRACT:
Digital filtering of digitally represented samples of an output analog signal may be greatly simplified when the required processing is done in a transformed domain instead of in the object domain. Such a transform is performed by converting blocks of samples ##EQU1## into blocks of signals ##EQU2## and vice versa where ##EQU3## It will be obvious that the filtering operation can be performed efficiently when the computing power required for the transforms is not too great or expensive.
It has been shown that whenever the number of samples N is the square of an integer M, any Fourier transform with ##EQU4## may be performed using a bank of very simple filters. However, the technique is not as efficient in reducing the number of required computing operations as is the Fast Fourier transform decomposition.
The present invention proposes a design using a bank of simple filters to adapt the above method to the computation of transform operations performed in a ring (e.g., Mersenne or Fermat transforms). The bank of filters avoids most of the drawbacks of the prior method and enables the use of multiplexing techniques to reduce the processing structure required for the operation.

REFERENCES:
patent: 3679882 (1972-07-01), McAuliffe
patent: 3900721 (1975-08-01), Speiser et al.
patent: 3920974 (1975-11-01), Means
C. M. Rader "Discrete Convolutions via Mersenne Transforms," IEEE Trans. on Computers, vol. C-21, No. 12, Dec. 1972, pp. 1269-1273.

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