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Signal processing with number theoretic transforms and limited word lengths

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2 Author(s)
Chevillat, P. ; IBM Zurich Research Laboratory, Rüschlikon, Switzerland ; Closs, F.

Number Theoretic Transforms (NTT's), unlike the Discrete Fourier Transform (DFT), are defined in finite rings and fields rather than in the field of complex numbers. Some NTT's have a transform structure like the Fast Fourier Transform (FFT) and can be used for fast digital signal processing. The computational effort and the signal-to-noise ratio (SNR) performance of linear filtering in finite rings and fields are investigated. In particular, the effect of limited word lengths, i.e., b \leq 16 , and long transform lengths on the SNR is analyzed. It is shown that for small word lengths and/or moderate to large transform lengths NTT filtering achieves a better SNR than FFT filtering with fixed-point arithmetic. Some new NTT's with a single- or mixed-radix fast transform structure are presented. While these NTT's may require special modulo arithmetic they achieve optimum transform length for any given word length b in the range 8 \leq b \leq 16 .

Published in:

Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '78.  (Volume:3 )

Date of Conference:

Apr 1978