## Practical Time-Frequency Analysis: Gabor and Wavelet Transforms, with an Implementation in STime frequency analysis has been the object of intense research activity in the last decade. This book gives a self-contained account of methods recently introduced to analyze mathematical functions and signals simultaneously in terms of time and frequency variables. The book gives a detailed presentation of the applications of these transforms to signal processing, emphasizing the continuous transforms and their applications to signal analysis problems, including estimation, denoising, detection, and synthesis. To help the reader perform these analyses, Practical Time-Frequency Analysis provides a set of useful tools in the form of a library of S functions, downloadable from the authors' Web sites in the United States and France.Key Features * Detailed presentation of the Wavelet and Gabor transforms * Applications to deterministic and random signal theory * Spectral analysis of nonstationary signals and processes * Numerous practical examples ranging from speech analysis to underwater acoustics, earthquake engineering, internet traffic, radar signal denoising, medical data interpretation, etc * Accompanying software and data sets, freely downloadable from the book's Web page |

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### Contents

25 | |

Gabor and Wavelet Transforms | 99 |

Signal Processing Applications | 219 |

The Swave Library | 355 |

Indexes | 471 |

Notation Index | 473 |

477 | |

S Functions and Utilities | 481 |

483 | |

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### Common terms and phrases

2D array algorithm applications approximation array containing autocovariance function basis bat sonar signal Brownian motion Chapter chirp coefﬁcients component compute consider continuous wavelet transform corresponding cost function covariance crazy climbers decomposition deﬁned deﬁnition discrete discussion domain dual wavelets dyadic wavelet transform equation example extrema Figure ﬁlters ﬁnite energy ﬁrst ﬁxed formula Fourier transform frequency function f Gabor functions Gaussian given Hurst exponent IEEE Trans inﬁnite integral kernel linear Mallat method Morlet wavelet noisy notation nvoice octave OPTIONAL ARGUMENTS original signal orthonormal orthonormal basis output parameter periodogram phase plot problem random reconstructed signal Remark REQUIRED ARGUMENTS ridge detection ridge samples sample points scaling function sequence signal f smoothing space speciﬁc spectral density spectral estimation spline stationary processes statistical subsampling Swave theorem time-frequency representation tion Transform Modulus transient USAGE values variable wavelet analysis wavelet packets wavelet spectrum white noise Wigner-Ville window