New optimization algorithms for designing wavelet scaling filters

In previous papers we introduced the generalized multiple exchange (GME) algorithm to design linear phase FIR filters, and the recursive GME (RGME) algorithm to design digital and analog IIR filters, and nonlinear phase FIR filters. The algorithms are based on the peak-constrained least-squares (PCLS) optimality criterion. In this paper we introduce three new algorithms to design wavelet scaling filters. The first algorithm designs PCLS valid half-band filters and is based on the GME algorithm. The second algorithm designs spectrally factored PCLS valid half-bound filters and is based on the RGME algorithm. The third algorithm designs orthogonal wavelet scaling filters and is based on the RGME algorithm. All three algorithms allow for filter specification tradeoffs that are characteristic of PCLS filters.