Fast trigonometric transforms and periodic orthogonal wavelet transforms are essential tools for numerous practical applications. It is very important that fast algorithms work stable in a floating point arithmetic. This survey paper presents recent results on the worst case analysis of roundoff errors occurring in floating point computation of fast Fourier transforms, fast cosine transforms, a...

Complex discrete wavelet transforms have significant advantages over real wavelet transforms for certain signal processing problems. Two approaches to the implementation of complex wavelet transforms have been proposed earlier. Both approaches require discrete-time allpass systems having approximately linear-phase and (fractional) delay. This paper compares the results when different allpass sy...

The main goal of the paper is to show that wavelet transforms and packets have the multiparametric representation in the form of a product of the rotation Jacobi matrices. These representations we call the third and the fourth canonical multiparametric form. Each multiparametric wavelet transform (MPWT) depends on several free Jacobi parameters. When parameters are changed multiparametric trans...

Let Mn,m be the space of real n × m matrices which can be identified with the Euclidean space R. We introduce continuous wavelet transforms on Mn,m with a multivalued scaling parameter represented by a positive definite symmetric matrix. These transforms agree with the polar decomposition on Mn,m and coincide with classical ones in the rank-one case m = 1. We prove an analog of Calderón’s repro...

ABSTIUCT In our previous work, we introduced a new class of nonstationary stochastic processes whose spectral representation is associated with the wavelet transforms and established a mathematical framework for the analysis of such processes 111. We refer to these processes as uffine stptionary processes. These processes are indexed by the affine p u p , or ax+b group, which can be though of a...

Let G = ( R∗+ × SO0(1, n) ) n Rn+1 be the Weyl-Poincaré group and KAN be the Iwasawa decomposition of SO0(1, n) with K = SO(n). Then the “affine Weyl-Poincaré group” Ga = ( R∗+ × AN ) n Rn+1 can be realized as the complex tube domain Π = Rn+1 + iC or the classical Cartan domain BDI(q = 2). The square-integrable representations of G and Ga give the admissible wavelets and wavelet transforms. An ...

introduction: studying long-term trend changes of meteorological parameters is one of the routine methods in atmospheric studies, especially in the climate change subject. among the meteorological parameters, temperature is always considered as one of the most atmospheric elements and studying it in order to gain a better understanding of the climate change phenomenon, has been effective. in ad...

With progress in radar systems, a number of methods have been developed for signal processing and detection in radars. A number of modern radar signal processing methods use time-frequency transforms, especially the wavelet transform (WT) which is a well-known linear transform. The interference canceling is one of the most important applications of the wavelet transform. In Ad-hoc detection met...