Symmetric basis functions and their unitary transforms

Authors:
N. D. Sinha;R. A. Haddad
Affiliations:
School of Electrical Engineering and Computer Science, Polytechnic University, Brooklyn, New York;School of Electrical Engineering and Computer Science, Polytechnic University, Brooklyn, New York
Venue:
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: image and multidimensional signal processing - Volume V
Year:
1993

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Abstract

We have generalized the scheme to generate new families of basis functions for the space L2[a, b] and from them obtained discrete unitary transforms by applying suitable sampling grids. The basis functions so generated can be used for the series expansion of signals and are algebraically related to one another via a positive trigonometric polynomial. The unitary transforms obtained from these functions have properties that are related to the symmetry of the function and the sampling grid that has been applied. Finally a transform from this family may be Chosen depending on the input signal characteristics making them useful in adaptive algorithms.