tailieunhanh - Phân tích tín hiệu P9

Non-Linear TirneFrequency Distributions In Chapters 7 and 8 twotime-frequencydistributions were discussed: the spectrogram and the scalogram. Both distributions are the result of linear filtering and subsequent forming of the squared magnitude. In this chapter time-frequency distributions derived in a different manner will be considered. Contrary to spectrograms and scalograms, their resolution is not restricted by the uncertainty principle. Although these methods do not yield positive distributions in all cases, they allow extremelygood insight into signal properties within certain applications. . | Signal Analysis Wavelets Filter Banks Time-Frequency Transforms and Applications. Alfred Mertins Copyright 1999 John Wiley Sons Ltd Print ISBN 0-471-98626-7 Electronic ISBN 0-470-84183-4 Chapter 9 Non-Linear Time- Frequency Distributions In Chapters 7 and 8 two time-frequency distributions were discussed the spectrogram and the scalogram. Both distributions are the result of linear filtering and subsequent forming of the squared magnitude. In this chapter time-frequency distributions derived in a different manner will be considered. Contrary to spectrograms and scalograms their resolution is not restricted by the uncertainty principle. Although these methods do not yield positive distributions in all cases they allow extremely good insight into signal properties within certain applications. The Ambiguity Function The goal of the following considerations is to describe the relationship between signals and their time as well as frequency-shifted versions. We start by looking at time and frequency shifts separately. Time-Shifted Signals. The distance d x xT between an energy signal x t and its time-shifted version a r t x t r is related to the autocorrelation function rxx r . Here the following holds cf. d xT x 2 2HXH2 -2 Jt rfx r 265 266 Chapter 9. Non-Linear Time-Frequency Distributions where oo rxz T XT X I x i x t r dt. J oo As explained in Section rfx r can also be understood as the inverse Fourier transform of the energy density spectrum Sxx w AT cư 2 1 f rfx r ejUT du Z7T J nn y . 9-3 1 oo X w X w e 7 du. J 0Q In applications in which the signal x t is transmitted and the time shift T is to be estimated from the received signal x t t it is important that x t and x t r are as dissimilar as possible for T 0. That is the transmitted signal i t should have an autocorrelation function that is as Dirac-shaped as possible. In the frequency domain this means that the energy density spectrum should be as constant as possible. Frequency-Shifted