Brief Notes in Advanced DSP: Fourier Analysis with MATLAB

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CRC Press, Apr 19, 2016 - Technology & Engineering - 354 pages
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Based on the authors’ research in Fourier analysis, Brief Notes in Advanced DSP: Fourier Analysis with MATLABŪ addresses many concepts and applications of digital signal processing (DSP). The included MATLABŪ codes illustrate how to apply the ideas in practice.

The book begins with the basic concept of the discrete Fourier transformation and its properties. It then describes lifting schemes, integer transformations, the discrete cosine transform, and the paired transform method for calculating the discrete Hadamard transform. The text also examines the decomposition of the 1D signal by so-called section basis signals as well as new forms of 2D signal/image representation and decomposition by direction signals/images. Focusing on Fourier transform wavelets and Givens–Haar transforms, the last chapter discusses the problem of signal multiresolution.

This book presents numerous interesting problems and concepts of unitary transformations, such as the Fourier, Hadamard, Hartley, Haar, paired, cosine, and new signal-induced transformations. It aids readers in using new forms and methods of signals and images in the frequency and frequency-and-time domains.

 

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Contents

Discrete Fourier Transform
1
Integer Fourier Transform
45
Cosine Transform
129
Hadamard Transform
185
Paired TransformBased Decomposition
243
Fourier Transform and Multiresolution
285
References
339
Index
347
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