Transforms and applications primer for engineers with examples and MATLAB

✍ Scribed by Poularikas, Alexander D

• Publisher: CRC Press
• Year: 2010
• Tongue: English
• Leaves: 570
• Series: Electrical engineering primer series
• Category: Library

✦ Table of Contents

Content: Signals and Systems Signals Circuit Elements and Equation Linear Mechanical and Rotational Mechanical Elements Discrete Equations and Systems Digital Simulation of Analog Systems Convolution of Analog Signals Convolution of Discrete Signals Fourier Series Fourier Series in a Complex Exponential Form Fourier Series in Trigonometric Form Waveform Symmetries Some Additional Features of Periodic Continuous Functions Fourier Transforms Other Forms of Fourier Transform Fourier Transform Examples Fourier Transform Properties Examples on Fourier Properties FT Examples of Singular Functions Duration of a Signal and the Uncertainty Principle Applications to Linear-Time Invariant Systems Applications to Communication Signals Signals, Noise, and Correlation Average Power Spectra, Random Signals, Input-Output Relations FT in Probability Theory Relatives to the Fourier Transform Infinite Fourier Sine Transform Infinite Fourier Cosine Transform Applications to Boundary-Value Problems Finite Sine Fourier Transform and Finite Cosine Fourier Transform Two-Dimensional Fourier Transform Sampling of Continuous Signals Fundamentals of Sampling The Sampling Theorem Discrete-Time Transforms Discrete-Time Fourier Transform Summary of DTFT Properties DTFT of Finite Time Sequences Frequency Response of LTI Discrete Systems Discrete Fourier Transform Summary of DFT Properties Multirate Digital Signal Processing and Spectra Appendix Proofs of DTFT Properties Proofs of DFT Properties Fast Fourier Transform Decimation in Time Procedure Laplace Transform One-Sided Laplace Transform Summary of the Laplace Transform Properties Systems Analysis: Transfer Functions of LTI Systems Inverse Laplace Transform Problem Solving with Laplace Transform Frequency Response of LTI Systems Pole Location and the Stability of LTI Systems Feedback for Linear Systems Bode Plots Inversion Integral Complex Integration and the Bilateral Laplace Transform State Space and State Equations The z-Transform 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 LTI Discrete-Time Dynamical Systems z-Transform and Random Processes Relationship between the Laplace and z-Transforms Relationship to the Fourier Transform Appendix Hilbert Transforms Definition Hilbert Transforms, Properties and the Analytic Signal Hilbert Transform Properties and Hilbert Pairs Appendices Index