IIR-Based ${\rm DT}{cal C}{\rm WTs}$ With Improved Analyticity and Frequency Selectivity

In this paper, a new class of DTCWTs with improved analyticity and frequency selectivity is proposed by using general IIR filters with numerator and denominator of different degree. In the common-factor technique proposed by Selesnick, the maximally flat allpass filter was used to satisfy the half-sample delay condition. Thus, to improve the analyticity of complex wavelets, we present a method for designing allpass filters with the specified degree of flatness and equiripple phase response in the approximation band. Furthermore, to improve the frequency selectivity of scaling lowpass filters, we locate the specified number of zeros at z = -1 and minimize the stopband error. The design methods proposed in this paper use the well-known Remez exchange algorithm to approximate the equiripple response. Therefore, a set of filter coefficients can be easily obtained by solving the eigenvalue problem. Finally, we investigate the performance on the proposed DTCWTs through several design examples. It is shown that the conventional DTCWTs proposed by Selesnick are only the special cases of DTCWTs proposed in this paper.