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.

[1]  Ali N. Akansu,et al.  Time-frequency localization in transforms, subbands, and wavelets: a critical review , 1993 .

[2]  P. Vilbe,et al.  On the uncertainty principle in discrete signals , 1992 .

[3]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[4]  Dennis Gabor,et al.  Theory of communication , 1946 .

[5]  A. Papoulis,et al.  The Fourier Integral and Its Applications , 1963 .

[6]  P. Urcun,et al.  A MUSICAM source codec for digital audio broadcasting and storage , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[7]  Claude Berrou,et al.  Coded orthogonal frequency division multiplex [TV broadcasting] , 1995, Proc. IEEE.

[8]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[9]  Truong Q. Nguyen,et al.  The theory and design of arbitrary-length cosine-modulated filter banks and wavelets, satisfying perfect reconstruction , 1996, IEEE Trans. Signal Process..

[10]  B. Floch,et al.  Coded orthogonal frequency division multiplex , 1995 .

[11]  Jean-Claude Belfiore,et al.  A Time-Frequency Well-localized Pulse for Multiple Carrier Transmission , 1997, Wirel. Pers. Commun..

[12]  Helmut Bölcskei,et al.  Equivalence of two methods for constructing tight Gabor frames , 2000, IEEE Signal Processing Letters.

[13]  P. Siohan,et al.  Analytical design for a family of cosine modulated filter banks , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[14]  Pierre Siohan,et al.  A family of extended Gaussian functions with a nearly optimal localization property , 1997 .

[15]  Milos Doroslovacki,et al.  Product of second moments in time and frequency for discrete-time signals and the uncertainty limit , 1998, Signal Process..