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Digital Signal processing is everywhere, it is pervasive and ubiquitous. Its methodologies are evolving and spreading its wings into many exciting new directions such as networking, bioinformatics, digital security and forensics, and spoken language. As a technology, it is a ”phantom technology” which is working from behind the scenes to make most of modern day devices work. Designed for both undergraduate and post graduate courses, this book provides a comprehensive insight into the linear algebra and optimization view of signal processing that can be readily extended to advanced image processing, wavelet theory and compressive sensing. This book shows how the entire class of problems in signal and image processing can be put in a linear algebra and optimization framework. Key Features: Only prerequisite is first year undergraduate mathematics. Signal Processing is now a tool for every engineer, therefore the book is written in such a way that it is accessible to students across the branches. Very simple exposition to latest developments in Variational signal and image processing. An introduction to level set theory and the latest convex formulation is presented. Introduction to compressed sensing, sparse signal processing and its associated mathematics. Applications in speech and character segmentation. All the illustration in the book along with the Matlab codes and Excel exercises are provided in the the book’s website http://nlp.amrita.edu:8080/book. About The Author Dr. K.P. Soman, (Ph.D., IIT Kharagpur) is Head, Centre for Excellence in Computational Engineering and Networking, Amrita Vishwa Vidyapeetham, Coimbatore. He has published/presented over 100 papers in international journals and conferences. His areas of interest include Compressed Sensing, Signal and Image Processing, Machine Learning, Software Defined Radio and Computational Linguistics. Dr. Soman has authored three books - Insight into Wavelets: From Theory to Practice (2010), Insight into Data Mining: Theory and Practice (2006), Machine Learning with SVM and Other Kernel Methods (2009). R. Ramanathan, (M.Tech) is Assistant Professor, Department of Electronics and Communication Engineering, Amrita Vishwa Vidyapeetham, Coimbatore. He has contributed around 26 technical papers in recent technologies like Support Vector Machines, Software Radio and Wavelets. His areas of interest include Computational Engineering, Optimization and Signal Processing for Wireless Communication. Table Of Contents Part – I Chapter 1: Signal Processing-An Introduction Chapter 2: Linear Algebra for Signal Processing Chapter 3: Complex Bases for Real Signals Chapter 4: Convolution Chapter 5: From DFT to FFT Chapter 6: Z Domain Representation of Signals Chapter 7: Digital Filter Design Chapter 8: Multirate Signal Processing Chapter 9: Introduction to Microsoft Excel Chapter 10: Excel for Plotting 1 D and 2 D Signals Chapter 11: Lab Exercises in Excel and Matlab Chapter 12: Sampling Fundamentals Part – II Chapter 13: Modern Measurements and Processing of Signals Chapter 14: Unconstrained and Constrained Optimization Algorithms Chapter 15: Total Variation Denoising Chapter 16: Sparse 1D Deconvolution for Signal Restoration Chapter 17: PDE and Image Processing Chapter 18: Calculus of Variation Chapter 19: Total Variational Methods for Image Denoising Chapter 20: Introduction to Image Inpainting Chapter 21: Nonlinear Diffusion: Algorithms, and Applications Chapter 22: Algorithms for Image Deblurring Chapter 23: Level Set Theory for Image Segmentation Chapter 24: Compressed Sensing and Sparse Signal Representation Chapter 25: Additional Topics in Image Processing Chapter 26: Speech Processing Chapter 27: Optical Character Recognition Appendix A Appendix B Index