Abstract. Gabor and wavelet methods are preferred to classical Fourier methods, whenever the time dependence of the analyzed signal is of the same importance as its frequency dependence. However, there exist strict limits to the maximal time-frequency resolution of these both transforms, similar to Heisenberg’s uncertainty principle in Fourier analysis. Results of this type are the subject of t...

We extend the ridgelet transform to the space of tempered Boehmians consistent with the ridgelet transform on the space of tempered distributions. We also prove that the extended ridgelet transform is continuous, linear, bijection and the extended adjoint ridgelet transform is also linear and continuous. AMS Mathematics Subject Classification (2010): 44A15, 44A35, 42C40

In this paper, formulas relating the Radon transform and Radon transform inversion to various wavelet and multiscale transformations, including the continuous wavelet transform, the semi{continuous wavelet transform of Mallat, steerable multiscale lters of Freeman and Adelson, and separable orthogonal and non{orthogonal wavelet bases, are given. The use of wavelets as a valuable tool in the loc...

We present a computational method for pattern discovery based on the application of the wavelet transform to symbolic representations of melodies or monophonic voices. We model the importance of a discovered pattern in terms of the compression ratio that can be achieved by using it to describe that part of the melody covered by its occurrences. The proposed method resembles that of paradigmatic...

We study the wavelet transform of functions invariant under a symmetry group, where the wavelet transform is associated to an irreducible unitary group representation. Among other results a new inversion formula and a new covariance principle are derived. As main examples we discuss the continuous wavelet transform and the short time Fourier transform of radially symmetric functions on R. 2000 ...