Tests of a new basis for signal processing

The Jacobi group G is a semidirect product of SL(2, R) and the three-dimensional Heisenberg group. This group acts on functions on the space H × C, where H is the upper half plane. The action includes both the windowed Fourier transform and the wavelet transform. As a result, Wallace [1] proposed using the Jacobi group for a signal processing scheme. In this paper, the action 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 are then used to reconstruct Chebyshev polynomials and sinc functions in order to test the effectiveness of using G for a signal processing algorithm.