A multiplicative Zac transform

Abstract

Summary form only given. A multiplicative Zac transform that plays the same role in analyzing affine group wavelets as the standard Zac transform plays in Heisenberg-Weyl wavelet theory has been defined in frequency space for causal signals. This construction is based on dilated complex exponentials that are eigenvectors of a sequence of dilation operators. Algorithms, based on the finite Fourier transform have been designed for analysis and synthesis of signals passing through the multiplicative Zac transform.<>