Cosine-modulated filter banks

The MDCT is known under the name Modulated Lapped Transform ([Malvar, 1990]) as well. Extensions using an overlap of more than a factor of two have been proposed [Vaupelt, 1991, Malvar, 1991] and used for coding of high quality audio [Vaupelt, 1991]. This type of filter banks can be described within the framework of cosine-modulated filter banks ([Koilpillai and Vaidyanathan, 1991][Ramstadt and T anem, 1991, Malvar, 1992]). 

In summary it can be stated that hybrid filter banks allow increased flexibility in the design by including the possibility to have different frequency resolutions at different frequencies. Another degree of freedom which is gained by using hybrid filter banks is the adaptive switching of the filter bank to different time/frequency behavior. On the downside, a somewhat increased complexity compared to solutions based on cosine-modulated filter banks is necessary to implement adaptive hybrid systems. 

Koilpillai and Vaidyanathan, 1991] Koilpillai, D. and Vaidyanathan, P. P. (1991). New Results on Cosine-Modulated FIR Filter Banks Satisfying Perfect Reconstruction. In Proc. IEEE Int. Conf. Acoust., Speech and Signal Proc, pages 1793 -1796. 

A limitation of this method is that the pitch period must be known exactly to obtain reliable estimates. The running DFT can be viewed as a filter bank where each filter is a cosine modulated version of a prototype filter given by a rectangular window of length N over the interval 0 < n < N. Based on this interpretation, an improvement in sine-wave parameter estimation can be made by generalizing the window shape as described in the following section. 

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See also in sourсe #XX -- [ ]

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