Higher density wavelet frames with symmetric low-pass and band-pass filters

This paper presents a new set of higher density wavelet frames with symmetric low-pass and band-pass wavelet filters. Based on the maximally flat low-pass linear-phase FIR filter and spectral factorization, two types of design approaches are proposed, which can respectively obtain odd-length FIR filters and even-length FIR filters. The two compact support wavelets respectively have a specified order of vanishing moments and a high degree of regularity. Several design examples are given. The denoising experiments show that the proposed wavelet frames have better shift invariance and denoising performance than the wavelet frames constructed by I.W. Selesnick. In engineering application, the proposed wavelet frame is applied to extract the fault feature of a roller bearing with out-race fault.