Design of finite impulse response digital filters with nonlinear phase response

Most of the existing literature on FIR digital filters is concerned with linear-phase (LP) filters. However, several papers have appeared on the subject of nonlinear-phase (NLP) filters, mainly proposing methods for designing minimum-phase filters, or approximating a desired phase response. In this paper, an investigation is made of one such method, based upon a selection of zeros from a prototype LP filter. It is shown that with respect to minimizing the order of a filter subject to given gain response specifications, this is the most efficient method for designing FIR filters. Coefficient quantization error is analyzed for filters generated by this method. A practical comparison is given between the resulting filter and the corresponding minimal order LP filter. It is shown that while most LP filters can be implemented more efficiently than NLP filters by taking into account the symmetry of their coefficients, for filters with very wide passband and for certain special purpose filters such as CCD and those used for filtering a delta-modulated or ADPCM signal, an NLP implementation is usually more efficient. In addition, an alternate design algorithm is proposed for NLP filters which decreases ripple magnitude. The resulting filters, while not of minimal order, can be efficiently implemented by decomposing the filter into LP stopband and NLP passband sections, which is especially attractive for narrow passbands.