Recursive structure for linear filtering using number theoretic transform
M. Bhattacharya, Jaakko T. Astola · 2002
Where speed of computation, i.e. data throughput, is not a constraint, it is feasible to implement digital signal processing algorithms in a bit serial fashion. One could employ look-up tables for realizing the difference equation eliminating the generally costly multiplier stage. We get a low power implementation as the power dissipation is quite low due to bit serial implementation and lower throughput rate of data. It is possible to implement filtering using number theoretic transform (NTT) for certain choices of modulus in structure that is completely different from the typical FFT structure, although the lengths considered are square numbers and quite composite. To mention a few advantages, there is no data index management in intermediate stages or twiddle factor multiplications and complex multiplications unlike typical FFT structures, low multiplication per point compared to FIR filtering, and low power consumption, while some marginal complexity due to modulo arithmetic remains.