Tests of a new basis for signal processing

The Jacobi group G is a semidirect product of SL(2,R) and the three-dimensi onal Heisenberg group. This group acts on functions on the space H x C, whe re H: is the upper half plane. The action includes both the windowed Fourie r transform and the wavelet transform. As a result, Wallace [1] proposed us ing the Jacobi group for a signal processing scheme. In this paper, the act ion of the Jacobi group is used to produce small bases of functions of one variable. Some properties of the basis functions are examined. The bases ar e then used to reconstruct Chebyshev polynomials and sine functions in orde r to test the effectiveness of using G for a signal processing algorithm. ( C) 2001 Elsevier Science Ltd. All rights reserved.