Cosine-modulated filterbanks based on extended Gaussian functions

A new family of cosine-modulated filterbanks based on functions called extended Gaussian functions (EGFs) is obtained. The design is particularly simple since it is mainly based on a closed-form expression. Nearly perfect reconstruction cosine-modulated filterbanks are obtained as well as guidelines to estimate the filterbank parameters. This analytical design method can be used to produce, with a controlled accuracy, filterbanks with practically no upper limitations in the number of coefficients and subbands. Furthermore, a slight modification of the prototype filter coefficients is sufficient to satisfy exactly the perfect reconstruction constraints. An analysis of the time-frequency localization of the discrete prototype filters also shows that under certain conditions, EGF prototypes are at less than 0.3% from the optimal upper bound.