Complex-valued M-band wavelets design

Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases offer a number of potential advantageous properties. For example, it has been suggested that the complex wavelets can be used as a vestigial sideband (VSB) filter in multiuser communications C. J. Zarowski (2000). In this paper, we make an extension to the method of Davidson, Luo and Wongf (2000). We present a general method to design optimal complex-valued M-band filters and M-band wavelets. This method is more efficient and accurate than the previous linear programming problem (LPP) methods. And some examples of optimal wavelet design are provided. We also analyze the tradeoff between the peak stop band level (PSL) and stop band energy ratio (SER) of the optimal filters. Because this is important in designing waveforms with prescribed spectral characteristics.