Amir-Homayoon Najmi - Böcker

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A comprehensive introduction to the mathematical principles and algorithms in statistical signal processing and modern neural networks. 

This text is an expanded version of a graduate course on advanced signal processing at the Johns Hopkins University Whiting school program for professionals with students from electrical engineering, physics, computer and data science, and mathematics backgrounds.  It covers the theory underlying applications in statistical signal processing including spectral estimation, linear prediction, adaptive filters, and optimal processing of uniform spatial arrays.  Unique among books on the subject, it also includes a comprehensive introduction to modern neural networks with examples in time series prediction and image classification.    

Coverage includes:

Mathematical structures of signal spaces and matrix factorizationslinear time-invariant systems and transformsLeast squares filtersRandom variables, estimation theory, and random processesSpectral estimation and autoregressive signal modelslinear prediction and adaptive filtersOptimal processing of linear arraysNeural networks

Introduced nearly three decades ago as a variable resolution alternative to the Fourier transform, a wavelet is a short oscillatory waveform for analysis of transients. The discrete wavelet transform has remarkable multi-resolution and energy-compaction properties. Amir-Homayoon Najmi's introduction to wavelet theory explains this mathematical concept clearly and succinctly. Wavelets are used in processing digital signals and imagery from myriad sources. They form the backbone of the JPEG2000 compression standard, and the Federal Bureau of Investigation uses biorthogonal wavelets to compress and store its vast database of fingerprints. Najmi provides the mathematics that demonstrate how wavelets work, describes how to construct them, and discusses their importance as a tool to investigate and process signals and imagery. He reviews key concepts such as frames, localizing transforms, orthogonal and biorthogonal bases, and multi-resolution. His examples include the Haar, the Shannon, and the Daubechies families of orthogonal and biorthogonal wavelets. Our capacity and need for collecting and transmitting digital data is increasing at an astonishing rate.So too is the importance of wavelets to anyone working with and analyzing digital data. Najmi's primer will be an indispensable resource for those in computer science, the physical sciences, applied mathematics, and engineering who wish to obtain an in-depth understanding and working knowledge of this fascinating and evolving field.