Cosine/Sine-Modulated Analysis/Synthesis Filter Banks

One of the topics in multi-rate digital signal processing is the theory and design of M-band (or M-channel) analysis and synthesis quadrature mirror filter (QMF) banks for sub-band signal decomposition and coding. They are also called M-band maximally decimated critically sampled QMF banks. The analysis QMF bank consists of M uniform and equally spaced channel filters to decompose the input signal into M sub-band signals. The synthesis QMF bank consists of channel filters to reconstruct the original signal exactly from sub-band signals, or to recover a signal which is nearly perfect approximation of the original signal. Historically, discovering the 2-band QMF banks in 1976 stimulated and started research activities leading to extending the theory of near-perfect and perfect reconstruction QMF banks for arbitrary number of sub-bands, to developing a family of near-perfect modulated filter banks (or pseudo-QMF banks) and perfect reconstruction modulated filter banks based on the concept of time domain aliasing cancellation.