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Discrete-Signal Analysis and Design
William E. Sabin (Author)
9780470187777, Wiley
Hardback, published 14 March 2008
192 pages
24.3 x 16.1 x 1.8 cm, 0.499 kg
“Discrete-Signal analysis and Design is written in an easy-to-follow, conversational style and supplies readers with a solid foundation for more advanced literature and software. It employs the occasional re-examination and reinforcement of particularly important concepts and each chapter contains self-study examples and full-page Mathcad Worksheets, worked-out and fully explained.” (International Journal Microstructure & Materials Properties, 2009)
A clear, step-by-step approach to practical uses of discrete-signal analysis and design, especially for communications and radio engineers This book provides an introduction to discrete-time and discrete-frequency signal processing, which is rapidly becoming an important, modern way to design and analyze electronics projects of all kinds. It presents discrete-signal processing concepts from the perspective of an experienced electronics or radio engineer, which is especially meaningful for practicing engineers, technicians, and students. The approach is almost entirely mathematical, but at a level that is suitable for undergraduate curriculums and also for independent, at-home study using a personal computer. Coverage includes: First principles, including the Discrete Fourier Transform (DFT) Sine, cosine, and theta Spectral leakage and aliasing Smoothing and windowing Multiplication and convolution Probability and correlation Power spectrum Hilbert transform The accompanying CD-ROM includes Mathcad® v.14 Academic Edition, which is reproduced with permission and has no time limitation for use, providing users with a sophisticated and world-famous tool for a wide range of applied mathematics capabilities. Discrete-Signal Analysis and Design is written in an easy-to-follow, conversational style and supplies readers with a solid foundation for more advanced literature and software. It employs occasional re-examination and reinforcement of particularly important concepts, and each chapter contains self-study examples and full-page Mathcad® Worksheets, worked-out and fully explained.
Preface xi Introduction 1 Goals of the Book Discrete Signals Advantages of Discrete-Signal Analysis and Design DFT and IDFT Mathcad Program MATLAB and Less Expensive Approaches Multisim Program from National Instruments Co. Mathtype Program LabVIEW Search Engines Personal Productivity Software Capability 1 First Principles 9 Sequence Structure in the Time and Frequency Domains Two-Sided Time and Frequency Discrete Fourier Transform Inverse Discrete Fourier Transform Frequency and Time Scaling Number of Samples Complex Frequency-Domain Sequences x(n) Versus Time and X(k) Versus Frequency 2 Sine, Cosine, and θ 27 One-Sided Sequences Combinations of Two-Sided Phasors Time and Spectrum Transformations Transforming Two-Sided Phasor Sequences into One-Sided Sine, Cosine, θ Example 2-1: Nonlinear Amplifier Distortion and Square Law Modulator Example 2-2: Analysis of the Ramp Function 3 Spectral Leakage and Aliasing 43 Spectral Leakage. Noninteger Values of Time x(n) and Frequency X(k) Example 3-1: Frequency Scaling to Reduce Leakage Aliasing in the Frequency Domain Example 3-2: Analysis of Frequency-Domain Aliasing Aliasing in the Time Domain 4 Smoothing and Windowing 61 Smoothing the Rectangular Window, Without Noise and with Noise Smoothed Sequences Near the Beginning and End Rectangular Window Hamming Window Hanning (Hann) Window Relative Merits of the Three Windows Scaling the Windows 5 Multiplication and Convolution 77 Sequence Multiplication Polynomial Multiplication Convolution Discrete Convolution Basic Equation Relating Convolution to Polynomial Multiplication “Fold and Slide” Concept Circular Discrete Convolution (Try to Avoid) Sequence Time and Phase Shift DFT and IDFT of Discrete Convolution Fig. 5-6. Compare Convolution and Multiplication Deconvolution 6 Probability and Correlation 95 Properties of a Discrete Sequence Expected Value of x(n) Include Some Additive Noise Envelope Detection of Noisy Sequence Average Power of Noiseless Sequence Power of Noisy Sequence Sequence Averaging Variance Gaussian (Normal) Distribution Cumulative Distribution Correlation and Covariance Autocorrelation Cross-Correlation Autocovariance Cross-Covariance Correlation Coefficient 7 The Power Spectrum 113 Finding the Power Spectrum Two-Sided Phasor Spectrum, One-Sided Power Spectrum Example 7-1: The Use of Eq. (7-2) Random Gaussian Noise Spectrum Measuring the Power Spectrum Spectrum Analyzer Example Wiener-Khintchine Theorem System Power Transfer Cross Power Spectrum Example of Calculating Phase Noise 8 The Hilbert Transform 129 The Perfect Hilbert Transformer Example of a Hilbert Transform of an Almost-Square Wave Smoothing of the Example Peaks in Hilbert of Square Wave Mathematics of the Hilbert Transform Analytic Signal Example 8-2: Construction of Analytic Signal Single-Sideband RF Signals SSB Design Basic All-Pass Network −90◦ Cascaded Phase Shift Audio Network Why the −90◦ Network Is Not Equivalent to a Hilbert Transformer Phasing Method SSB Transmitter Filter Method SSB Transmitter Phasing Method SSB Receiver Filter Method SSB Receiver Appendix: Additional Discrete-Signal Analysis and Design Information 153 Discrete Derivative State-Variable Solutions Using the Discrete Derivative to Solve a Time Domain Discrete Differential Equation Glossary 163 Index 171
Subject Areas: Electronics & communications engineering [TJ]
