New Algorithm for Designing FIR Filters with Power-of-Two Coefficients

The paper presents an algorithm for optimal vector quantization of an FIR filter´s coefficients using SPT format. The measure of quality of quantization is the Euclidean distance between of the set of coefficients and its approximations. Because of the Parseval theorem minimization of the Euclidean distance between two sets of coefficients of the FIR filter is equivalent to minimization of the mean square distance between frequency characteristic of filters. The idea of the quantization algorithm is very similar to the idea of the Huffman coding. The algorithm was tested with the mini-max error based designs of FIR filter obtained by the means of the Parks-McClellan methodology.