Differential DFT digital filtering device

Details Differential DFT digital filtering device Differential DFT digital filtering device

1977-01-26

1978-10-03

Malzahn, David H.

Boots, shoes, and leggings

G06F 738

Patent

active

041187849

ABSTRACT:
When using the family of Discrete Fourier Transform (DFT) and Finite Field Transforms, the continuous convolution process corresponding to the filtering operation is converted into a series of finite aperiodic convolutions which are in turn computed as a series of circular convolutions by dividing the sequences to be convolved into blocks and lengthening these blocks either by appending zeros (overlap-add) or by repeating part of the sequences (overlap-save).
This causes a serious increase in the number of operations over what would have been required if the filtering process had been a true circular convolution.
This disclosure provides means for performing the filtering operation without appending any zeros and without repeating part of the sequences.
The flow of input samples is split into fixed length blocks which are simultaneously fed into two circular convolutors using different DFT's. More particularly, one convolutor operates in a conventional DFT domain, i.e., a DFT providing: ##EQU1## Where x.sub.n is the n.sup.th input signal sample and a.sub.l the l.sup.th filter coefficient.
The second convolutor operates in a modified DFT domain, i.e.: ##EQU2## The modified convolutor provides a first series of normal terms belonging to the required filtering operation and a second series of parasitic terms multiplied by R.sup.N. So long as R.sup.N is different from unity, very simple operations will remove the parasitic terms and provide the filtered sample.

REFERENCES:
patent: 3679882 (1972-07-01), McAuliffe
patent: 3925646 (1975-12-01), Richardson et al.
patent: 4006351 (1977-02-01), Constant
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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