A Novel Variable Filter Band Discrete Wavelet Transform: Theory And Principle

It is well-known that a mother wavelet for the discrete wavelet transform (DWT) has the band-pass filter characteristic with octave width in the frequency domain and can be used for octave analysis. However, it is possible that the octave analysis is not necessarily the most suitable to match the analysis signal. In this study, in order to construct the most suitable basis to match the analysis signal, a novel variable-filter band discrete wavelet transform (VFB-DWT) is proposed. It is achieved by using variable-band filters instead of conventional decomposition and reconstruction sequences, which are designed in consideration of the real signal characteristics. Additionally, it is proven that perfect reconstruction of the analysis signal by VFB-DWT is guaranteed using the perfect shift invariant theorem that underlies the theory of the PTI-CDWT having base DWT.