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RESEARCH PRODUCT

Introduction to Digital Signal Processing

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Signal processing deals with the representation, transformation, and manipulation of signals and the information they contain. Typical examples include extracting the pure signals from a mixture observation (a field commonly known as deconvolution) or particular signal (frequency) components from noisy observations (generally known as filtering). This chapter outlines the basics of signal processing and then introduces the more advanced concepts of time‐frequency and time‐scale representations, as well as emerging fields of compressed sensing and multidimensional signal processing. When moving to multidimensional signal processing, a modern approach is taken from the point of view of statistical (machine) learning. An interesting branch of multidimensional signals and systems analysis is that of spectral analysis on manifolds. The chapter presents the spectral analysis of a mesh by using a combinational graph Laplacian and a geometric mesh Laplacian. Finally, the chapter gives a selected set of illustrative examples to review the discussed basic concepts of signal processing and standard techniques.