Discrete-Signal Analysis and Design

William E. Sabin, MSEE, Life Member IEEE, has worked at a professional engineering level in the electronics industry for forty years in almost all areas of signal processing, including analog, discrete, and digital. He has coedited three books on the subject of radio systems and circuits and is the author of about forty technical articles in electronics journals.

• Preface xiIntroduction 1Goals of the BookDiscrete SignalsAdvantages of Discrete-Signal Analysis and DesignDFT and IDFTMathcad ProgramMATLAB and Less Expensive ApproachesMultisim Program from National Instruments Co.Mathtype ProgramLabVIEWSearch EnginesPersonal Productivity Software Capability1 First Principles 9Sequence Structure in the Time and Frequency DomainsTwo-Sided Time and FrequencyDiscrete Fourier TransformInverse Discrete Fourier TransformFrequency and Time ScalingNumber of SamplesComplex Frequency-Domain Sequencesx(n) Versus Time and X(k) Versus Frequency2 Sine, Cosine, and θ 27One-Sided SequencesCombinations of Two-Sided PhasorsTime and Spectrum TransformationsTransforming Two-Sided Phasor Sequences into One-Sided Sine, Cosine, θExample 2-1: Nonlinear Amplifier Distortion and Square Law ModulatorExample 2-2: Analysis of the Ramp Function3 Spectral Leakage and Aliasing 43Spectral Leakage. Noninteger Values of Time x(n) and Frequency X(k)Example 3-1: Frequency Scaling to Reduce Leakage Aliasing in the Frequency DomainExample 3-2: Analysis of Frequency-Domain Aliasing Aliasing in the Time Domain4 Smoothing and Windowing 61Smoothing the Rectangular Window, Without Noise and with NoiseSmoothed Sequences Near the Beginning and EndRectangular WindowHamming WindowHanning (Hann) WindowRelative Merits of the Three WindowsScaling the Windows5 Multiplication and Convolution 77Sequence MultiplicationPolynomial MultiplicationConvolutionDiscrete Convolution Basic EquationRelating Convolution to Polynomial Multiplication“Fold and Slide” ConceptCircular Discrete Convolution (Try to Avoid)Sequence Time and Phase ShiftDFT and IDFT of Discrete ConvolutionFig. 5-6. Compare Convolution and MultiplicationDeconvolution6 Probability and Correlation 95Properties of a Discrete SequenceExpected Value of x(n)Include Some Additive NoiseEnvelope Detection of Noisy SequenceAverage Power of Noiseless SequencePower of Noisy SequenceSequence AveragingVarianceGaussian (Normal) DistributionCumulative DistributionCorrelation and CovarianceAutocorrelationCross-CorrelationAutocovarianceCross-CovarianceCorrelation Coefficient7 The Power Spectrum 113Finding the Power SpectrumTwo-Sided Phasor Spectrum, One-Sided Power SpectrumExample 7-1: The Use of Eq. (7-2)Random Gaussian Noise SpectrumMeasuring the Power SpectrumSpectrum Analyzer ExampleWiener-Khintchine TheoremSystem Power TransferCross Power SpectrumExample of Calculating Phase Noise8 The Hilbert Transform 129The Perfect Hilbert TransformerExample of a Hilbert Transform of an Almost-Square WaveSmoothing of the ExamplePeaks in Hilbert of Square WaveMathematics of the Hilbert TransformAnalytic SignalExample 8-2: Construction of Analytic SignalSingle-Sideband RF SignalsSSB DesignBasic All-Pass Network−90◦ Cascaded Phase Shift Audio NetworkWhy the −90◦ Network Is Not Equivalent to a Hilbert TransformerPhasing Method SSB Transmitter Filter Method SSB TransmitterPhasing Method SSB ReceiverFilter Method SSB ReceiverAppendix: Additional Discrete-Signal Analysis and Design Information 153Discrete DerivativeState-Variable SolutionsUsing the Discrete Derivative to Solve a Time Domain Discrete Differential EquationGlossary 163Index 171

“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)"This volume is valuable for students, academic libraries, mathematicians, and working professionals, especially Mathead users." (CHOICE, August 2008)