A Proof of the Necessary Condition for Perfect Reconstruction of Signals Using the Two-channel Wavelet Filter Bank
Waldemar Rakowski · Bulletin of the Polish Academy of Sciences Technical Sciences · 2003
Wavelet representation of signals and images is very useful for compression purposes. To obtain a wavelet representation by splitting a digital signal into two subsampled sygnals in a two-channel filter bank, the filters must satisfy perfect reconstruction conditions. This paper presents a theorem that formulates perfect reconstruction conditions for two-channel filter bank and a complete proof of both necessary and sufficient conditions. Additional requirements for filters guaranteeing the existence of the wavelets are reviewed.