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On discrete Fourier analysis of amplitude and phase modulated signals

Waldemar Popiński (2012)

Applicationes Mathematicae

In this work the problem of characterization of the Discrete Fourier Transform (DFT) spectrum of an original complex-valued signal o t , t=0,1,...,n-1, modulated by random fluctuations of its amplitude and/or phase is investigated. It is assumed that the amplitude and/or phase of the signal at discrete times of observation are distorted by realizations of uncorrelated random variables or randomly permuted sequences of complex numbers. We derive the expected values and bounds on the variances of such...

Ternary wavelets and their applications to signal compression

Ghulam Mustafa, Falai Chen, Zhangjin Huang (2004)

International Journal of Applied Mathematics and Computer Science

We introduce ternary wavelets, based on an interpolating 4-point C^2 ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). However, for compressing regular signals we further classify ternary wavelets into 'odd ternary' and 'even...

Wavelet transform and binary coalescence detection

Jean-Michel Innocent, Bruno Torrésani (1997)

Banach Center Publications

We give a short account of some time-frequency methods which are relevant in the context of gravity waves detection. We focus on the case of wavelet analysis which we believe is particularly appropriate. We show how wavelet transforms can lead to efficient algorithms for detection and parameter estimation of binary coalescence signals. In addition, we give in an appendix some of the ingredients needed for the construction of discrete wavelet decompositions and corresponding fast algorithms.

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