Design of Cosine-Modulated Filter Banks for Partial Spectrum Reconstruction

In this paper, we present a new technique to design filterbanks that allows the partial reconstruction of the spectrum of a signal. In several applications, there is the need of either decreasing the sampling rate of a signal preserving part of its spectrum or increasing the sampling rate with minimum spectrum degradation. In this paper, we will develop a method based on cosine-modulated filterbanks to accomplish this task. An analysis filterbank is used to divide the spectrum into subbands. Another filterbank, with a different number of channels, is used to reconstruct the spectrum contained in part of (or all) the subbands. The ratio between the input and output sampling rates is equal to the ratio between the analysis downsampling and synthesis upsampling factors. The problem becomes that of designing the prototypes of the analysis and synthesis filterbanks. Several numerical examples of filterbanks design are presented.