Cosine-Modulated Filterbanks Based on Extended

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 proto- type 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. Index Terms—Cosine-modulated filterbanks, Gaussian function, localization. more, as shown in (5), it can also be used to derive a closed-form expression that describes a new family of functions called ex- tended Gaussian functions (EGFs). In this paper, a discrete ver- sion of the EGF is used to design filterbanks by means of the two following procedures. • The impulse response of the protototype filter is directly derived from the continous-time expression of the EGF; under certain conditions, the corresponding impulse and frequency responses closely approximate the ideal EGF in the time and frequency domain. The overall back-to-back system leads to a nearly perfect reconstruction modulated filter (PRMF) bank. Furthermore, practical design rules that yield good estimates of the necessary filter lengths and number of bands to satisfy all our requirements with a given accuracy are also included. • The impulse response of the prototype filter is optimized in order to exactly satisfy the PR condition. The ideal time and frequency shapes of the EGF are only approximated, but the PR property is structurally ensured.