Signals and Systems Primer with MATLAB®

Abstract

SIGNALS AND THEIR FUNCTIONAL REPRESENTATION Some applications involving signals Fundamental representation of simple time signals Signal conditioning and manipulation Representation of signals Appendix 1: Elementary matrix algebra Appendix 2: Complex numbers Appendix 1 Problems Appendix 2 Problems LINEAR CONTINUOUS-TIME SYSTEMS Properties of systems Modeling simple continuous systems Solutions of first-order systems Evaluation of integration constants: initial conditions Block diagram representation Convolution and correlation of continuous-time signals Impulse response DISCRETE SYSTEMS Discrete systems and equations Digital simulation of analog systems Digital simulation of higher-order differential equations Convolution of discrete-time signals Appendix 1: Method of variation of parameters Appendix 2: Euler's approximation for differential equations PERIODIC CONTINUOUS SIGNALS AND THEIR SPECTRUMS Complex functions Fourier series of continuous functions Features of periodic continuous functions Linear systems with periodic inputs NONPERIODIC SIGNALS AND THEIR FOURIER TRANSFORM Direct and inverse Fourier transform Properties of Fourier transforms Some special Fourier transform pairs Effects of truncation and Gibbs' phenomenon Linear time-invariant filters Appendix SAMPLING OF CONTINUOUS SIGNALS Fundamentals of sampling The sampling theorem DISCRETE-TIME TRANSFORMS Discrete-time Fourier transform (DTFT) Summary of DTFT properties DTFT of finite time sequences Frequency response of linear time-invariant (LTI) discrete systems The discrete Fourier transform (DFT) Summary of the DFT properties Multirate digital signal processing Appendix 1: Proofs of the DTFT properties Appendix 2: Proofs of DFT properties Appendix 3: Fast Fourier transform (FFT) LAPLACE TRANSFORM One-sided Laplace transform Summary of the Laplace transform properties Systems analysis: transfer functions of LTI systems Inverse Laplace transform (ILT) Problem solving with Laplace transform Frequency response of LTI systems Pole location and the stability of LTI systems Feedback for linear systems Bode plots Appendix: Proofs of Laplace transform properties THE Z-TRANSFORM, DIFFERENCE EQUATIONS, AND DISCRETE SYSTEMS The z-transform Convergence of the z-transform Properties of the z-transform z-Transform pairs Inverse z-transform Transfer function Frequency response of first-order discrete systems Frequency response of higher-order digital systems z-Transform solution of first-order difference equations Higher-order difference equations Appendix: Proofs of the z-transform properties ANALOG FILTER DESIGN General aspects of filters Butterworth filter Chebyshev low-pass filter Phase characteristics Frequency transformations Analog filter design using MATLAB functions FINITE IMPULSE RESPONSE (FIR) FILTERS Properties of FIR filters FIR filters using the Fourier series approach FIR filters using windows Prescribed filter specifications using a Kaiser window MATLAB FIR filter design INFINITE IMPULSE RESPONSE (IIR) FILTERS The impulse-invariant method approximation in the time domain Bilinear transformation Frequency transformation for digital filters Recursive versus nonrecursive design RANDOM VARIABLES, SEQUENCES, AND POWER SPECTRA DENSITIES Random signals and distributions Averages Stationary processes Special random signals and probability density functions Wiener-Kintchin relations Filtering random processes Nonparametric spectra estimation LEAST SQUARE SYSTEM DESIGN, WIENER FILTER, AND THE LMS FILTER The least-squares technique The mean square error Wiener filtering examples The least mean square (LMS) algorithm Examples using the LMS algorithm APPENDIX A: MATHEMATICAL FORMULAS Trigonometric identities Orthigonality Summation of trigonometric forms Summation formulas Series expansions Logarithms Some definite integrals APPENDIX B: SUGGESTIONS AND EXPLANATIONS FOR MATLAB USE Creating a directory Help Save and load MATLAB as calculator Variable names Complex numbers Array indexing Extracting and inserting numbers in arrays Vectorization Matrices Produce a periodic function Script files Functions Subplots Figures Changing the scales of the axes of a figure Writing Greek letters Subscripts and superscripts Lines in plots INDEX Each chapter features Important Definitions and Concepts as well as Problems.