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