Two approaches for fixed-point filter design: "bit-flipping" algorithm and constrained downhill simplex method

This paper presents two techniques for the design of digital filters with wordlength-constrained coefficients, the bit-flipping algorithm improved since it was first presented in 1994 and the downhill simplex method modified to deliver fixed-point filter coefficients. Both techniques can be applied to design of filter coefficients from scratch or to the optimisation of their floating-point versions. Both methods presented in this paper have been tested on the two-path polyphase half-band lowpass filter design problem. However, both these techniques can be used with almost no alteration, for general constrained coefficient digital design.