Device generating a digital filter and a discrete convolution fu

Details Device generating a digital filter and a discrete convolution fu Device generating a digital filter and a discrete convolution fu

1976-03-10

1977-12-13

Malzahn, David H.

Boots, shoes, and leggings

364724, G06F 1534

Patent

active

040630820

ABSTRACT:
A digital filter is described which is based on the use of the so-called primitive roots transform and its inverse. This transform converts a series of binary numbers {a.sub.n } into a transformed series ##EQU1## WHERE G IS A PRIMITIVE ROOT OF A PRIME NUMBER P, AND THE VALUES BETWEEN SUPERFLUOUS PARENTHESES ARE TAKEN MODULO P. Said filter is provided with input means for applying fixed length data blocks made of a group of input samples appended with an equal number of zeros to the input of at least one circular convolutor. This convolutor is provided with accumulating means for generating multiples of each a.sub.n term, adding means for generating said A.sub.k terms by adding successively provided multiples of a.sub.n to selected partial terms of A.sub.k, and means for storing said partial A.sub.k terms as they are formed. There is also a device for storing the Primitive Roots transform B.sub.k of the set of filter coefficients appended with an equal number of zeros, a multiplier means for performing the operation C.sub.k = A.sub.k .multidot. B.sub.k modulo p, and an invertor for inverting the resulting C.sub.k bits. An inverse transformer having an accumulating means for generating multiples of the terms C.sub.k, adding means for generating the terms of the inverse transforms c.sub.n by adding selected multiples of C.sub.k and for storing said terms of said transforms is also provided. The filter also has an adding means for adding inverse transforms deriving from two consecutive blocks to generate a series of output terms representing a filtered signal.

REFERENCES:
patent: 3808412 (1974-04-01), Smith
patent: 3872290 (1975-03-01), Crooke et al.
patent: 3925646 (1975-12-01), Richardson et al.
patent: 3926367 (1975-12-01), Bond et al.
J. L. Shanks and T. W. Cairns, "Use of a Digital Convolution Device to Perform Recursive Filtering and the Cooley-Tukey Algorithm" IEEE Trans. on Computers, Oct. 1968, pp. 943-949.

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