QMF Filters and Wavelets

The compression of certain signals, such as speech, sound, or images, involves sub‐band decomposition combined with sampling rate reduction and reconstruction from sub‐bands after storage or transmission. The simplest approach, which minimizes computational load, consists of selecting identical linear phase filters. The coefficient calculation procedure is the minimum phase technique for finite impulse response filters. The objective of the wavelet theory is the representation of signals in the time‐frequency domain. The accuracy of the reconstruction is evaluated by computing the impulse response of the analysis/synthesis system. The factorization of the half‐band filter can also be realized in lattice representation, canceling every other coefficient. The accuracy of the reconstruction is evaluated by computing the impulse response of the analysis/synthesis system.