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.
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.
Biography
Alexander D. Poularikas
"The book is written with a high pedagogical mastership; the style of exposition is clear and attractive, the typographical presentation is excellent . . . Much valuable information is contained in the book at a moderate mathematical level . . . we think the present volume is an excellent book on SS and can be a serious candidate for a reference book in presenting the SS domain."
– Dumitru Stanomir,in Zentralblatt Math, 2009
