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Fermat Transform Filters with Overflow Detection

IP.com Disclosure Number: IPCOM000086067D
Original Publication Date: 1976-Jul-01
Included in the Prior Art Database: 2005-Mar-03
Document File: 2 page(s) / 41K

Publishing Venue

IBM

Related People

Nussbaumer, H: AUTHOR

Abstract

It is now well known that digital filters can be implemented with considerable savings in the number of arithmetic operations by using discrete transforms.

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Fermat Transform Filters with Overflow Detection

It is now well known that digital filters can be implemented with considerable savings in the number of arithmetic operations by using discrete transforms.

It has been shown by Rader ("Discrete Convolutions via Mersenne Transforms", C.M. Rader - IEEE Transactions on Computers - Vol. C21 No. 12 - December 1972) and also by Agarwal and Burrus ("Fast Convolution Using Fermat Number Transforms with Applications to Digital Filtering" - R.C. Agarwal and C.S. Burrus - IEEE Transactions on Acoustics, Speech and Signal Processing - Vol. ASSP 22 No. 2 - April 1974) that Fermat transforms provide an interesting solution for such an implementation.

The purpose here is to describe a circuit which detects overflows and, therefore, adjusts the input signal levels close to saturation, so as to operate the filter with full available dynamic range.

The input signal enters a digital automatic gain control circuit (AGC).

The output of the AGC drives either directly or through other circuit a conventional pseudo Mersenne transformer MT1, which computes the transforms {A(k)} of the input samples {an} according to:

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The transforms {B(k)} of the filter coefficient {bn} are precomputed and stored in read-only memory ROM1. The A(k) and B(k) are multiplied in multiplier M1 to provide C(k) = A(k) . B(k). The C(k) enters a conventional inverse pseudo- Mersenne transform circuit IMT1 which delivers dm terms computed modulo (2/2/q...