Multiband least squares FIR filter design

Abstract

This paper gives two methods for the least squares approximation design of FIR digital filters. They both allow multiple pass and stop bands and arbitrary transition bands, all with explicit control of band edges. The first method is as simple to use as a window method. This design method builds up an optimal multiband frequency response by sequentially adding and subtracting optimal lowpass filters with transition bands. However, it assumes the ideal response has spline transition functions and does not allow error weighting. The second method allows different weights in the multiple passbands, stopbands and transition bands but it requires numerical solution of simultaneous equations which may be ill-conditioned. These methods compliment the Parks-McClellan algorithm which minimizes the Chebyshev error.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>