Multidimensional Discrete Unitary Transforms
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Multidimensional Discrete Unitary Transforms
This reference presents a more efficient, flexible, and manageable approach to unitary transform calculation and examines novel concepts in the design, classification, and management of fast algorithms for different transforms in one-, two-, and multidimensional cases. Illustrating methods to construct new unitary transforms for best algorithm selection and development in real-world applications, the book contains a wide range of examples to compare the efficacy of different algorithms in a variety of one-, two-, and three-dimensional cases. Multidimensional Discrete Unitary Transforms builds progressively from simple representative cases to higher levels of generalization.
Transforms and Applications Handbook
Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.
Brief Notes in Advanced DSP
Based on the authors’ research in Fourier analysis, Brief Notes in Advanced DSP: Fourier Analysis with MATLAB® addresses many concepts and applications of digital signal processing (DSP). The included MATLAB® 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.