6.7 COSINE MODULATED PERFECT RECONSTRUCTION (PR) M-BAND BANKS AND THE MODIFIED DISCRETE COSINE TRANSFORM (MDCT)
Although PQMF banks have been used quite successfully in perceptual audio coders, the overall system design still must compensate for the inherent distortion induced by the lack of perfect reconstruction to avoid audible artifacts in the codec output. The compensation strategy may be a simple one (e.g., increased prototype filter length), but perfect reconstruction is actually preferable because it constrains the sources of output distortion to the quantization stage. Beginning in the early 1990s, independent work by Malvar [Malv90b], Ramstad [Rams91], and Koilpillai and Vaidyanathan [Koil91] [Koil92] showed that generalized perfect reconstruction (PR) cosine modulated filter banks are possible by appropriately constraining the prototype lowpass filter, w(n), and synthesis filters, gk(n), for . In particular, perfect reconstruction is guaranteed for a cosine-modulated filter bank with analysis filters, hk(n), given by Eqs. (6.13) and (6.15) if four conditions are satisfied. First, the length, L, of the window, w(n), must be integer multiple of the number of subbands, i.e.,
where the parameter m is an integer greater than zero. Next, the synthesis filters, gk(n), must be ...