DiscreteSignal Analysis and Design
DiscreteSignal Analysis and Design
ISBN: 9780470187777 February 2008 192 Pages
Description
This book provides an introduction to discretetime and discretefrequency signal processing, which is rapidly becoming an important, modern way to design and analyze electronics projects of all kinds. It presents discretesignal 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, athome 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 CDROM includes Mathcad® v.14 Academic Edition, which is reproduced with permission and has no time limitation for use, providing users with a sophisticated and worldfamous tool for a wide range of applied mathematics capabilities.
DiscreteSignal Analysis and Design is written in an easytofollow, conversational style and supplies readers with a solid foundation for more advanced literature and software. It employs occasional reexamination and reinforcement of particularly important concepts, and each chapter contains selfstudy examples and fullpage Mathcad® Worksheets, workedout and fully explained.
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Table of contents
Preface xi
Introduction 1
Goals of the Book
Discrete Signals
Advantages of DiscreteSignal 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
TwoSided Time and Frequency
Discrete Fourier Transform
Inverse Discrete Fourier Transform
Frequency and Time Scaling
Number of Samples
Complex FrequencyDomain Sequences
x(n) Versus Time and X(k) Versus Frequency
2 Sine, Cosine, and θ 27
OneSided Sequences
Combinations of TwoSided Phasors
Time and Spectrum Transformations
Transforming TwoSided Phasor Sequences into OneSided Sine, Cosine, θ
Example 21: Nonlinear Amplifier Distortion and Square Law Modulator
Example 22: Analysis of the Ramp Function
3 Spectral Leakage and Aliasing 43
Spectral Leakage. Noninteger Values of Time x(n) and Frequency X(k)
Example 31: Frequency Scaling to Reduce Leakage Aliasing in the Frequency Domain
Example 32: Analysis of FrequencyDomain 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. 56. 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
CrossCorrelation
Autocovariance
CrossCovariance
Correlation Coefficient
7 The Power Spectrum 113
Finding the Power Spectrum
TwoSided Phasor Spectrum, OneSided Power Spectrum
Example 71: The Use of Eq. (72)
Random Gaussian Noise Spectrum
Measuring the Power Spectrum
Spectrum Analyzer Example
WienerKhintchine 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 AlmostSquare Wave
Smoothing of the Example
Peaks in Hilbert of Square Wave
Mathematics of the Hilbert Transform
Analytic Signal
Example 82: Construction of Analytic Signal
SingleSideband RF Signals
SSB Design
Basic AllPass 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 DiscreteSignal Analysis and Design Information 153
Discrete Derivative
StateVariable Solutions
Using the Discrete Derivative to Solve a Time Domain Discrete Differential Equation
Glossary 163
Index 171
Reviews
“DiscreteSignal analysis and Design is written in an easytofollow, conversational style and supplies readers with a solid foundation for more advanced literature and software. It employs the occasional reexamination and reinforcement of particularly important concepts and each chapter contains selfstudy examples and fullpage Mathcad Worksheets, workedout and fully explained.” (International Journal Microstructure & Materials Properties, 2009)
"This volume is valuable for students, academic libraries, mathematicians, and working professionals, especially Mathead users." (CHOICE, August 2008)Features
 Every chapter includes examples of practical uses of Discrete Signal Analysis & Design.
 Presents introductory digital signal processing concepts presented in a unique way that will be useful to graduate students; written by an experienced radio engineer.
 Includes Mathcad 14.0 for Students software giving practicing engineers and students alike all the tools they need to use this book. This software package is useful for the buyer long after they have mastered the text.
 This Mathcad 14.0 for Students software package offers significant personal and process productivity advantages for product development, engineering design projects and hundreds of other applications where calculations are key. This is not a timed out version of this product. It is the actual software package and the user receives a single user license.