Signals, systems, and transforms : concise coverage from theory to application / Fernand Cohen.

Cover -- Title Page -- Copyright Page -- Dedication Page -- Contents -- Preface -- Acknowledgments -- List of Symbols -- Chapter 1 Signals and Systems -- 1.1 Different Types of Signals -- 1.1.1 Causal, Anticausal, and Noncausal Signals -- 1.2 Symmetry in Signals -- 1.3 Singularity Functions -- 1.3.1 Impulse Function -- 1.3.2 Step Function -- 1.3.3 Rectangular Function -- 1.3.4 Ramp Function -- 1.3.5 Triangular Function -- 1.4 Transforming a Signal -- 1.4.1 Time Transformation -- 1.4.2 Amplitude Transformation -- 1.5 Characterizing a System and System's Properties -- 1.5.1 Linearity

1.5.2 Time Invariance -- 1.5.3 Invertibility -- 1.5.4 Causality -- 1.5.5 Bounded-Input Bounded-Output Stability -- 1.6 Impulse Response of an LTI System -- 1.6.1 Convolution Integral and Sum -- 1.6.2 Step and Ramp Responses -- 1.7 Impulse Response of LTI, RL, or RC Circuit -- 1.8 Second-Order Systems -- 1.9 Impulse Response of Rational Systems -- 1.10 Deconvolution -- 1.11 Chapter Summary -- Problems -- Chapter 2 Fourier Series (FS) -- 2.1 Development of Fourier Series: A Historical Perspective -- 2.2 Vector and Function Spaces -- 2.2.1 Geometric Projection and Dot Product

2.2.2 Function Space and Dot Product -- 2.3 Sinusoidal Functions -- 2.4 Fourier Series Expansion -- 2.4.1 Existence of Fourier Series -- 2.5 Fourier Series of Certain Signals and Properties -- 2.5.1 Train of Impulse Function -- 2.5.2 Shifting Property -- 2.5.3 Derivative Property -- 2.6 Spectral Representation of Periodic Functions -- 2.7 Fourier Series for Discrete Periodic Signals -- 2.7.1 2D Discrete Periodic Signal -- 2.8 Signal and Image Compression -- 2.8.1 Lossy Compression -- 2.9 Fourier Descriptors for Boundary Representation -- 2.10 Chapter Summary -- Problems -- 2.A Appendix

3.6 Parseval's Theorem -- 3.7 FT for Discrete Signals (DTFT) -- 3.7.1 Inverse DTFT -- 3.7.2 Properties of DTFT -- 3.7.2.1 Shifting Property -- 3.7.2.2 Derivative Property -- 3.7.2.3 Summation Property -- 3.8 Parseval's Theorem for DTFT -- 3.9 Discrete Rational System Approximation to a Continuous Rational System -- 3.10 Phasors and FT -- 3.11 FT in Medical Imaging -- 3.11.1 Projection Theorem -- 3.11.1.1 Projection Slice Theorem -- 3.12 Chapter Summary -- Problems -- References -- Chapter 4 DFT and FFT -- 4.1 Development of Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT)

Concise, linear textbook exploring the fundamentals of signals and systems analysis using Fourier tools and generalized Fourier tools Signals, Systems, and Transforms covers the fundamentals of analyzing analog and discrete signals and systems in various domains using Fourier and generalized Fourier tools. The book shows how these tool elements are interconnected and weaves them into a sequential coherent story, with each element leading to the next, helping readers more easily grasp newer material due to previously developed concepts. Practically, the book examines how the theory applies to various fields ranging from biomedical imaging to filter designs for audio and video signals. The book includes interesting examples of the theories presented in the textbook for hands-on learning, as well as a lab section in MATLAB, where the reader is shown simulated examples and asked to perform certain tasks using simple MATLAB codes and functions. This book condenses material usually expressed in 800-1200 pages into approximately one-fourth of that length by capitalizing on how the various Fourier transforms relate and by unifying the treatment of the analog and discrete transforms. Signals, Systems, and Transforms includes information on: Laplace transform (LT) and Z-transform (ZT) as generalized Fourier transform. It then uses the concepts of transforms in the analysis of linear systems with rational Laplace and Z-transform The discrete Fourier transform (DFT) and its fast computation using fast Fourier transform (FFT) as a sampler in the Fourier domain Sampling of double-sided lowpass and bandpass signals (double- and single-sided) using concepts of modulation and Hilbert transform (HT) Quantization of signals, covering optimal quantizers, uniform quantizers, and compandors It introduces Singular Value Decomposition (SVD) as a subcase of optimal quantizers Unitary (energy-preserving) transforms such as the suboptimal cosine transforms Signals, Systems, and Transforms provides all of the necessary knowledge for electrical and computer engineering students to master fundamental tools related to the subject and be able to branch into the fascinating fields of signal processing and modeling, signal and system control, and power.

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