Method for implementing a multiplier-less FIR filter

摘要

A method for implementing a multiplier-less FIR filter is disclosed, in which the FIR filter performs the convolution of $H\left(z\right)=\sum _{k=0}^{N-1}{h}_k{z}^{-k},$ where h_k is the k-th coefficient of the FIR filter. The dynamic range of the filter coefficients is compressed by a transformation: $H^{\text{'}}\left(z\right)=H\left(z\right)\frac{\prod _{i=1}^{m-1}{\left(1+{\mathrm{alpha}}_i{z}^{-\mathrm{beta}}\right)}^m}{\prod _{i=1}^{m-1}{\left(1+{\mathrm{alpha}}_i{z}^{-\mathrm{beta}}\right)}^m},$ where parameters alpha and beta are chosen depending on filter type, -1<=alpha_i<=1, and m denotes iteration numbers of coefficient operation of transformation, so as to avoid the serious quantization error caused by the phenomenon of SPT distribution. Then, the compressed coefficients are quantized into SPT numbers, and the coefficients are optimized by removing redundant STP numbers.