Signals and Systems Primer with MATLAB

Taking a pedagogical approach, the author builds a solid foundation in signal processing as well as analog and digital systems. The book first introduces orthogonal signals, linear and time-invariant continuous-time systems, discrete-type systems and their solution, periodic signals represented by Fourier series, Gibbs's phenomenon, and the sampling theorem. After chapters on various transforms, the book discusses analog filter design, both finite and infinite impulse response digital filters, random digital signal processing, including the nonparametric spectral estimation. The final chapter characterizes different types of filtering and their uses, specifically, the use of Wiener filtering and least mean squares filtering.

Signals and Systems Primer with MATLAB® equally emphasizes the fundamentals of both analog and digital signals and systems. To ensure insight into the basic concepts and methods, the text presents a variety of examples that illustrate a wide range of applications, from microelectromechanical to worldwide communication systems. It also provides MATLAB functions and procedures for practice and verification of these concepts.Taking a pedagogical approach, the author builds a solid foundation in signal processing as well as analog and digital systems. The book first introduces orthogonal signals, linear and time-invariant continuous-time systems, discrete-type systems, periodic signals represented by Fourier series, Gibbs's phenomenon, and the sampling theorem. After chapters on various transforms, the book discusses analog filter design, both finite and infinite impulse response digital filters, and the fundamentals of random digital signal processing, including the nonparametric spectral estimation. The final chapter presents different types of filtering and their uses for random digital signal processing, specifically, the use of Wiener filtering and least mean squares filtering. Balancing the study of signals with system modeling and interactions, this text will help readers accurately develop mathematical representations of systems.

SIGNALS AND THEIR FUNCTIONAL REPRESENTATION Some applications involving signals Fundamental representation of simple time signalsSignal conditioning and manipulationRepresentation of signalsAppendix 1: Elementary matrix algebraAppendix 2: Complex numbersAppendix 1 ProblemsAppendix 2 ProblemsLINEAR CONTINUOUS-TIME SYSTEMSProperties of systems Modeling simple continuous systemsSolutions of first-order systemsEvaluation of integration constants: initial conditionsBlock diagram representationConvolution and correlation of continuous-time signalsImpulse responseDISCRETE SYSTEMSDiscrete systems and equations Digital simulation of analog systems Digital simulation of higher-order differential equationsConvolution of discrete-time signalsAppendix 1: Method of variation of parameters Appendix 2: Euler's approximation for differential equationsPERIODIC CONTINUOUS SIGNALS AND THEIR SPECTRUMSComplex functionsFourier series of continuous functionsFeatures of periodic continuous functionsLinear systems with periodic inputs NONPERIODIC SIGNALS AND THEIR FOURIER TRANSFORM Direct and inverse Fourier transformProperties of Fourier transformsSome special Fourier transform pairs Effects of truncation and Gibbs' phenomenon Linear time-invariant filtersAppendix SAMPLING OF CONTINUOUS SIGNALSFundamentals of samplingThe sampling theoremDISCRETE-TIME TRANSFORMSDiscrete-time Fourier transform (DTFT)Summary of DTFT propertiesDTFT of finite time sequencesFrequency response of linear time-invariant (LTI) discrete systemsThe discrete Fourier transform (DFT) Summary of the DFT properties Multirate digital signal processingAppendix 1: Proofs of the DTFT propertiesAppendix 2: Proofs of DFT propertiesAppendix 3: Fast Fourier transform (FFT)LAPLACE TRANSFORM One-sided Laplace transformSummary of the Laplace transform propertiesSystems analysis: transfer functions of LTI systemsInverse Laplace transform (ILT)Problem solving with Laplace transform Frequency response of LTI systemsPole location and the stability of LTI systemsFeedback for linear systemsBode plotsAppendix: Proofs of Laplace transform propertiesTHE Z-TRANSFORM, DIFFERENCE EQUATIONS, AND DISCRETE SYSTEMS The z-transformConvergence of the z-transformProperties of the z-transformz-Transform pairsInverse z-transform Transfer functionFrequency response of first-order discrete systemsFrequency response of higher-order digital systemsz-Transform solution of first-order difference equations Higher-order difference equationsAppendix: Proofs of the z-transform propertiesANALOG FILTER DESIGNGeneral aspects of filtersButterworth filter Chebyshev low-pass filterPhase characteristics Frequency transformationsAnalog filter design using MATLAB functionsFINITE IMPULSE RESPONSE (FIR) FILTERSProperties of FIR filtersFIR filters using the Fourier series approachFIR filters using windowsPrescribed filter specifications using a Kaiser window MATLAB FIR filter designINFINITE IMPULSE RESPONSE (IIR) FILTERS The impulse-invariant method approximation in the time domain Bilinear transformation Frequency transformation for digital filtersRecursive versus nonrecursive designRANDOM VARIABLES, SEQUENCES, AND POWER SPECTRA DENSITIES Random signals and distributionsAveragesStationary processesSpecial random signals and probability density functionsWiener-Kintchin relations Filtering random processesNonparametric spectra estimationLEAST SQUARE SYSTEM DESIGN, WIENER FILTER, AND THE LMS FILTERThe least-squares techniqueThe mean square errorWiener filtering examplesThe least mean square (LMS) algorithmExamples using the LMS algorithm APPENDIX A: MATHEMATICAL FORMULAS Trigonometric identities OrthigonalitySummation of trigonometric forms Summation formulasSeries expansions Logarithms Some definite integralsAPPENDIX B: SUGGESTIONS AND EXPLANATIONS FOR MATLAB USECreating a directoryHelpSave and load MATLAB as calculatorVariable names Complex numbers Array indexing Extracting and inserting numbers in arrays Vectorization Matrices Produce a periodic functionScript filesFunctions Subplots Figures Changing the scales of the axes of a figureWriting Greek letters Subscripts and superscripts Lines in plotsINDEXEach chapter features Important Definitions and Concepts as well as Problems.