Design of nonuniform cosine-modulated filter-banks with the perfect-reconstruction property and arbitrary filter lengths (Q2373616)

Filter banks (FB) are an arrangement of lowpass, band pass and highpass filters used in the spectral decomposition and composition of signals. They play an important role in audio and image coding. Most of them include changes of the sampling rate what led to the denomination of multi-rate systems. The signal to be analyzed is decomposed in \(M\) parallel channels so that these systems are also termed as multi-channel FB. Among them, one distinguishes the class of cosine-modulated filter CM (CMFB). In the usual CMFB arrangement, all the filters are derived from two finite-impulse response ones, \(h(n)\) and \(f(n)\) prototypes, through a cosine-like envelope modulation, whence its denomination. In the standard, the so-called uniform CMFB, the length of each signal on the channel must have a prescribed value. It is worthy to point out that the CMFB approach insures the perfect reconstruction (PR) condition, this fact meaning that the summation of all the channel contributions at the output provides a delayed replica of the input signal. In our days, this approach is used in MPEG audio coding. In some applications, by example in audio signal processing, a non-uniform frequency splitting is desired because of the non-uniform spacing of the critical bands. To meet these conditions, the present paper gives a complete answer in the class of PR condition, i.e. providing a design method for CMFB with arbitrary length off components. The approach is based on merging the components of a usual CMFB with a set of transmultiplexers. The idea of the method is based on a property found by the authors related to the ratio of the number of channels and the number of transmultiplexers. The numerical experiments given in the paper validate the proposed approach. We think the paper represents a nice contribution in the area of CMFB theory.