Titlebook: Wavelet Transforms and Time-Frequency Signal Analysis; Lokenath Debnath Book 2001 Springer Science+Business Media New York 2001 Fourier an

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The Uncertainty Principle for the Short-Time Fourier Transform and Wavelet Transformoduct in terms of the uncertainty product of the signal and window. Although the uncertainty product of the spectrogram is not the sum of the uncertainty products of the window and signal, nonetheless, we show that the global uncertainty product has to be greater than one. We also derive local uncer

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Quadratic Time-Frequency Analysis of Linear Time-Varying Systemss chapter, we study TF weighting and displacement effects using known and novel quadratic TF representations of LTV systems. In particular, we define and study two novel TF representations termed “input Wigner distribution” (IWD) and “output Wigner distribution” (OWD). The interpretations, various e

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Inequalities in Mellin-Fourier Signal Analysisand analytic signals. In this chapter, limitations for the simultaneous localization of scale transform pairs are investigated. A number of inequalities are established and discussed, based on various measures of spread (Heisenberg-type inequalities for variance-like measures and Hirschman-type ineq

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Introduction to Time-Frequency Signal Analysissing of signals with time-varying spectral characteristics. This chapter presents fundamental principles of TFSA and reviews the main contributions to the field, including the most recent advances, such as polynomial Wigner—Ville distributions (PWVD), the high time-frequency resolution B-distributio

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Reduced Interference Time-Frequency Distributions: Scaled Decompositions and Interpretationsle solutions that utilize special sets of orthonormally related windows to realize Cohen’s class of time-frequency distributions (TFDs) are proposed. This is accomplished by decomposing the kernel of the distribution in terms of the set of analysis windows to obtain short-time Fourier transforms (ST

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Book 2001. In an effort to inform researchers in mathematics, physics, statistics, computer science, and engineering and to stimulate furtherresearch, an NSF-CBMS Research Conference on Wavelet Analysis was organized at the University of Central Florida in May 1998. Many distinguished mathematicians and scie