Signals, Systems, Transforms, and Digital Signal Processing with MATLAB (Hardcover)

Continuous-Time and Discrete-Time Signals and SystemsIntroductionContinuous-Time SignalsPeriodic FunctionsUnit Step FunctionGraphical Representation of FunctionsEven and Odd Parts of a FunctionDirac-Delta ImpulseBasic Properties of the Dirac-Delta ImpulseOther Important Properties of the ImpulseContinuous-Time SystemsCausality, StabilityExamples of Electrical Continuous-Time SystemsMechanical SystemsTransfer Function and Frequency ResponseConvolution and CorrelationA Right-Sided and a Left-Sided FunctionConvolution with an Impulse and Its DerivativesAdditional Convolution PropertiesCorrelation FunctionProperties of the Correlation FunctionGraphical InterpretationCorrelation of Periodic FunctionsAverage, Energy and Power of Continuous-Time SignalsDiscrete-Time SignalsPeriodicityDifference EquationsEven/Odd DecompositionAverage Value, Energy and Power SequencesCausality, StabilityProblemsAnswers to Selected ProblemsFourier Series ExpansionTrigonometric Fourier SeriesExponential Fourier SeriesExponential versus Trigonometric SeriesPeriodicity of Fourier SeriesDirichlet Conditions and Function DiscontinuityProof of the Exponential Series ExpansionAnalysis Interval versus Function PeriodFourier Series as a Discrete-Frequency SpectrumMeaning of Negative FrequenciesProperties of Fourier SeriesDifferentiation of Discontinuous FunctionsFourier Series of an Impulse TrainExpansion into Cosine or Sine Fourier SeriesDeducing a Function Form from Its ExpansionTruncated Sinusoid Spectral LeakageThe Period of a Composite Sinusoidal SignalPassage through a Linear SystemParseval’s RelationsUse of Power Series ExpansionInverse Fourier SeriesProblemsAnswers to Selected ProblemsLaplace TransformIntroductionBilateral Laplace TransformConditions of Existence of Laplace TransformBasic Laplace TransformsNotes on the ROC of Laplace TransformProperties of Laplace TransformApplications of the Differentiation PropertyTransform of Right-Sided Periodic FunctionsConvolution in Laplace DomainCauchy’s Residue TheoremInverse Laplace TransformCase of Conjugate PolesThe Expansion Theorem of HeavisideApplication to Transfer Function and Impulse ResponseInverse Transform by Differentiation and IntegrationUnilateral Laplace TransformGamma FunctionTable of Additional Laplace TransformsProblemsAnswers to Selected ProblemsFourier TransformDefinition of the Fourier TransformFourier Transform as a Function of fFrom Fourier Series to Fourier TransformConditions of Existence of the Fourier TransformTable of Properties of the Fourier TransformSystem Frequency ResponseEven?Odd Decomposition of a Real FunctionCausal Real FunctionsTransform of the Dirac-Delta ImpulseTransform of a Complex Exponential and SinusoidSign FunctionUnit Step FunctionCausal SinusoidTable of Fourier Transforms of Basic FunctionsRelation between Fourier and Laplace TransformsRelation to Laplace Transform with Poles on Imaginary AxisConvolution in TimeLinear System Input?Output RelationConvolution in FrequencyParseval’s TheoremEnergy Spectral DensityAverage Value versus Fourier TransformFourier Transform of a Periodic FunctionImpulse TrainFourier Transform of Powers of TimeSystem Response to a Sinusoidal InputStability of a Linear SystemFourier Series versus Transform of Periodic FunctionsTransform of a Train of RectanglesFourier Transform of a Truncated SinusoidGaussian Function Laplace and Fourier TransformInverse Transform by Series ExpansionFourier Transform in ω and fFourier Transform of the Correlation FunctionIdeal Filters Impulse ResponseTime and Frequency Domain SamplingIdeal SamplingReconstruction of a Signal from its SamplesOther Sampling SystemsIdeal Sampling of a Bandpass SignalSampling an Arbitrary SignalSampling the Fourier TransformProblemsAnswers to Selected ProblemsSystem Modeling, Time and Frequency ResponseTransfer FunctionBlock Diagram ReductionGalvanometerDC MotorA Speed-Control SystemHomologyTransient and Steady-State ResponseStep Response of Linear SystemsFirst Order SystemSecond Order System ModelSettling TimeSecond Order System Frequency ResponseCase of a Double PoleThe Over-Damped CaseEvaluation of the OvershootCausal System Response to an Arbitrary InputSystem Response to a Causal Periodic InputResponse to a Causal Sinusoidal InputFrequency Response PlotsDecibels, Octaves, DecadesAsymptotic Frequency ResponseBode Plot of a Composite Linear SystemGraphical Representation of a System FunctionVectorial Evaluation of ResiduesVectorial Evaluation of the Frequency ResponseA First Order All-Pass SystemFiltering Properties of Basic CircuitsLowpass First Order FilterMinimum Phase SystemsGeneral Order All-Pass SystemsSignal GenerationApplication of Laplace Transform to Differential EquationsTransformation of Partial Differential EquationsProblemsAnswers to Selected ProblemsDiscrete-Time Signals and SystemsIntroductionLinear Time-Invariant SystemsLinear Constant-Coefficient Difference EquationsThe z-TransformConvergence of the z-TransformInverse z-TransformInverse z-Transform by Partial Fraction ExpansionInversion by Long DivisionInversion by a Power Series ExpansionInversion by Geometric Series SummationTable of Basic z-TransformsProperties of the z-TransformGeometric Evaluation of Frequency ResponseComb FiltersCausality and StabilityDelayed Response and Group DelayDiscrete-Time Convolution and CorrelationDiscrete-Time Correlation in One DimensionConvolution and Correlation as MultiplicationsResponse of a Linear System to a SinusoidNotes on the Cross-Correlation of SequencesLTI System Input/Output Correlation SequencesEnergy and Power Spectral DensityTwo-Dimensional SignalsLinear Systems, Convolution and CorrelationCorrelation of Two-Dimensional SignalsIIR and FIR Digital FiltersDiscrete-Time All-Pass SystemsMinimum-Phase and Inverse SystemUnilateral z-TransformProblemsAnswers to Selected ProblemsDiscrete-Time Fourier TransformLaplace, Fourier and z-Transform RelationsDiscrete-Time Processing of Continuous-Time SignalsA/D ConversionQuantization ErrorD/A ConversionContinuous versus Discrete Signal ProcessingInterlacing with ZerosSampling Rate ConversionFourier Transform of a Periodic SequenceTable of Discrete-Time Fourier TransformsReconstruction of the Continuous-Time SignalStability of a Linear SystemTable of Discrete-Time Fourier Transform PropertiesParseval’s TheoremFourier Series and Transform DualityDiscrete Fourier TransformDiscrete Fourier SeriesDFT of a Sinusoidal SignalDeducing the z-Transform from the DFTDFT versus DFSProperties of DFS and DFTCircular ConvolutionCircular Convolution Using the DFTSampling the SpectrumTable of Properties of DFSShift in Time and Circular ShiftTable of DFT PropertiesZero PaddingDiscrete z-TransformFast Fourier TransformAn Algorithm for a Wired-In Radix-2 ProcessorFactorization of the FFT to a Higher RadixFeedback Elimination for High-Speed Signal ProcessingProblemsAnswers to Selected ProblemsState Space ModelingIntroductionNote on NotationState Space ModelSystem Transfer FunctionSystem Response with Initial ConditionsJordan Canonical Form of State Space ModelEigenvalues and EigenvectorsMatrix DiagonalizationSimilarity Transformation of a State Space ModelSolution of the State EquationsGeneral Jordan Canonical FormCircuit Analysis by Laplace Transform and State VariablesTrajectories of a Second Order SystemSecond Order System ModelingTransformation of Trajectories between PlanesDiscrete-Time SystemsSolution of the State EquationsTransfer FunctionChange of VariablesSecond Canonical Form State Space ModelProblemsAnswers to Selected ProblemsFilters of Continuous-Time DomainLowpass ApproximationButterworth ApproximationDenormalization of Butterworth Filter PrototypeDenormalized Transfer FunctionThe Case ε 6= 1Butterworth Filter Order FormulaNomographsChebyshev ApproximationPass-Band RippleTransfer Function of the Chebyshev FilterMaxima and Minima of Chebyshev Filter ResponseThe Value of ε as a Function of Pass-Band RippleEvaluation of Chebyshev Filter GainChebyshev Filter TablesChebyshev Filter OrderDenormalization of Chebyshev Filter PrototypeChebyshev’s Approximation: Second FormResponse Decay of Butterworth and Chebyshev FiltersChebyshev Filter NomographElliptic FiltersProperties, Poles and Zeros of the sn FunctionPole Zero Alignment and Mapping of Elliptic FilterPoles of H(s)Zeros and Poles of G(ω)Zeros, Maxima and Minima of the Magnitude SpectrumPoints of Maxima/MinimaElliptic Filter NomographN = 9 ExampleTables of Elliptic FiltersBessel’s Constant Delay FiltersA Note on Continued Fraction ExpansionEvaluating the Filter DelayBessel Filter Quality Factor and Natural FrequencyMaximal Flatness of Bessel and Butterworth ResponseBessel Filter’s Delay and Magnitude ResponseDenormalization and Deviation from Ideal ResponseBessel Filter’s Magnitude and DelayBessel Filter’s Butterworth Asymptotic FormDelay of Bessel?Butterworth Asymptotic Form FilterDelay Plots of Butterworth Asymptotic Form Bessel FilterBessel Filters Frequency Normalized FormPoles and Zeros of Asymptotic and Frequency Normalized Bessel Filter FormsResponse and Delay of Normalized Form Bessel FilterBessel Frequency Normalized Form Attenuation SettingBessel Filter NomographFrequency TransformationsLowpass to Bandpass TransformationLowpass to Band-Stop TransformationLowpass to Highpass TransformationNote on Lowpass to Normalized Band-Stop TransformationWindowsRectangular WindowTriangle (Bartlett) WindowHanning WindowHamming WindowProblemsAnswers to Selected ProblemsPassive and Active FiltersDesign of Passive FiltersDesign of Passive Ladder Lowpass FiltersAnalysis of a General Order Passive Ladder NetworkInput Impedance of a Single-Resistance Terminated NetworkEvaluation of the Ladder Network ComponentsMatrix Evaluation of Input ImpedanceBessel Filter Passive Ladder NetworksTables of Single-Resistance Ladder Network ComponentsDesign of Doubly Terminated Passive LC Ladder NetworksTables of Double-Resistance Terminated Ladder Network ComponentsClosed Forms for Circuit Element ValuesElliptic Filter Realization as a Passive Ladder NetworkTable of Elliptic Filter Passive Network ComponentsElement Replacement for Frequency TransformationRealization of a General Order Active FilterInverting IntegratorBiquadratic Transfer FunctionsGeneral Biquad RealizationFirst Order Filter RealizationA Biquadratic Transfer Function RealizationSallen?Key CircuitProblemsAnswers to Selected ProblemsDigital FiltersIntroductionSignal Flow GraphsIIR Filter ModelsFirst Canonical FormTranspositionSecond Canonical FormTransposition of the Second Canonical FormStructures Based on Poles and ZerosCascaded FormParallel FormMatrix RepresentationFinite Impulse Response (FIR) FiltersLinear Phase FIR FiltersConversion of Continuous-Time to Discrete-Time FilterImpulse Invariance ApproachImpulse Invariance Approach CorrectedBackward-Rectangular ApproximationForward Rectangular and Trapezoidal ApproximationsBilinear TransformLattice FiltersFinite Impulse Response All-Zero Lattice StructuresOne-Zero FIR FilterTwo-Zeros FIR FilterGeneral Order All-Zero FIR FilterAll-Pole FilterFirst Order One-Pole FilterSecond Order All-Pole FilterGeneral Order All-Pole FilterPole-Zero IIR Lattice FilterAll-Pass Filter RealizationSchur?Cohn Stability CriterionFrequency TransformationsLeast Squares Digital Filter DesignPad´e ApproximationError Minimization in Prony’s MethodFIR Inverse Filter DesignImpulse Response of Ideal FiltersSpectral LeakageWindowsIdeal Digital Filters Rectangular WindowHanning WindowHamming WindowTriangular WindowComparison of Windows Spectral ParametersLinear-Phase FIR Filter Design Using WindowsEven- and Odd-Symmetric FIR Filter DesignLinear Phase FIR Filter RealizationSampling the Unit CircleImpulse Response Evaluation from Unit Circle SamplesProblemsAnswers to Selected ProblemsEnergy and Power Spectral DensitiesEnergy Spectral DensityAverage, Energy and Power of Continuous-Time SignalsDiscrete-Time SignalsEnergy SignalsAutocorrelation of Energy SignalsEnergy Signal through a Linear SystemImpulsive and Discrete-Time Energy SignalsPower SignalsCross-CorrelationPower Spectrum Conversion of a Linear SystemImpulsive and Discrete-Time Power SignalsPeriodic SignalsPower Spectral Density of an Impulse TrainAverage, Energy and Power of a SequenceEnergy Spectral Density of a SequenceAutocorrelation of an Energy SequencePower Density of a SequencePassage through a Linear SystemProblemsAnswers to Selected ProblemsIntroduction to Communication SystemsIntroductionAmplitude Modulation (AM) of Continuous-Time SignalsFrequency ModulationDiscrete SignalsDigital Communication SystemsPCM-TDM SystemsFrequency Division Multiplexing (FDM)ProblemsAnswers to Selected ProblemsFourier-, Laplace- and z-Related TransformsWalsh TransformRademacher and Haar FunctionsWalsh FunctionsThe Walsh (Sequency) OrderDyadic (Paley) OrderNatural (Hadamard) OrderDiscrete Walsh TransformDiscrete-Time Walsh TransformDiscrete-Time Walsh?Hadamard TransformNatural (Hadamard) Order Fast Walsh?Hadamard TransformDyadic (Paley) Order Fast Walsh?Hadamard TransformSequency Ordered Fast Walsh?Hadamard TransformGeneralized Walsh TransformNatural OrderGeneralized Sequency OrderGeneralized Walsh?Paley (p-adic) TransformWalsh?Kaczmarz TransformGeneralized Walsh Factorizations for Parallel ProcessingGeneralized Walsh Natural Order GWN MatrixGeneralized Walsh?Paley GWP Transformation MatrixGWK Transformation MatrixHigh Speed Optimal Generalized Walsh FactorizationsGWN Optimal FactorizationGWP Optimal FactorizationGWK Optimal FactorizationKarhunen Lo`eve TransformHilbert TransformHilbert TransformerDiscrete Hilbert TransformHartley TransformDiscrete Hartley TransformMellin TransformMellin Transform of ejxHankel TransformFourier Cosine TransformDiscrete Cosine Transform (DCT)Fractional Fourier TransformDiscrete Fractional Fourier TransformTwo-Dimensional TransformsTwo-Dimensional Fourier TransformContinuous-Time Domain Hilbert Transform RelationsHI (jω) versus HR(jω) with No Poles on AxisCase of Poles on the Imaginary AxisHilbert Transform Closed FormsWiener?Lee TransformsDiscrete-Time Domain Hilbert Transform RelationsProblemsAnswers to Selected ProblemsDigital Signal Processors: Architecture, Logic DesignIntroductionSystems for the Representation of NumbersConversion from Decimal to BinaryIntegers, Fractions and the Binary PointRepresentation of Negative NumbersInteger and Fractional Representation of Signed NumbersAdditionSubtractionFull Adder CellAddition/Subtraction Implementation in 2’s ComplementControlled Add/Subtract (CAS) CellMultiplication of Unsigned NumbersMultiplier Implementation3-D MultiplierA Direct Approach to 2’s Complement MultiplicationDivisionCellular Array for Nonrestoring DivisionCarry Look Ahead (CLA) Cell2’s Complement Nonrestoring DivisionConvergence DivisionEvaluation of the nth RootFunction Generation by Chebyshev Series ExpansionAn Alternative Approach to Chebyshev Series ExpansionFloating Point Number RepresentationSquare Root EvaluationCellular Array for Nonrestoring Square Root ExtractionBinary Coded Decimal (BCD) RepresentationMemory ElementsDesign of Synchronous Sequential CircuitsRealization of a Counter Using T Flip-FlopsState MinimizationAsynchronous Sequential MachinesState ReductionControl Counter Design for Generator of Prime NumbersFast Transform ProcessorsProgrammable Logic Arrays (PLAs)Field Programmable Gate Arrays (FPGAs)DSP with Xilinx FPGAsTexas Instruments TMS320C6713B Floating-Point DSPCentral Processing Unit (CPU)CPU Data Paths and ControlInstruction SyntaxTMS320C6000 Control Register FileAddressing Mode Register (AMR)Syntax for Load/Store Address GenerationProgramming the T.I. DSPA Simple C ProgramThe Generated Assembly CodeFibonacci Series in C Calling Assembly-Language FunctionFinite Impulse Response (FIR) FilterInfinite Impulse Response (IIR) Filter on the DSPReal-Time DSP Applications Using MATLAB?SimulinkDetailed Steps for DSP Programming in C++ and SimulinkMOS FET Logic Circuit RealizationProblemsAnswers to Selected ProblemsRandom Signal ProcessingNonparametric Methods of Power Spectrum EstimationCorrelation of Continuous-Time Random SignalsPassage through an LTI SystemWiener Filtering in Continuous-Time DomainCausal Wiener FilterRandom SequencesFrom Statistical to Time AveragesCorrelation and Covariance in z-DomainRandom Signal Passage through an LTI SystemPSD Estimation of Discrete-Time Random SequencesFast Fourier Transform (FFT) Evaluation of the PeriodogramParametric Methods for PSD EstimationThe Yule?Walker EquationsSystem Modeling for Linear Prediction, Adaptive Filtering and Spectrum EstimationWiener and Least-Squares ModelsWiener FilteringLeast-Squares FilteringForward Linear PredictionBackward Linear PredictionLattice MA FIR Filter RealizationAR Lattice of Order pARMA(p, q) ProcessPower Spectrum EstimationFIR Wiener Filtering of Noisy SignalsTwo-Sided IIR Wiener FilteringCausal IIR Wiener FilterWavelet TransformDiscrete Wavelet TransformImportant Signal Processing MATLAB FunctionslpcYulewalkdfiltlogspaceFIR Filter Designfir2Power Spectrum Estimation Using MATLABParametric Modeling FunctionspronyA z-Domain Counterpart to Prony’s MethodProblemsAnswers to Selected ProblemsDistributionsIntroductionDistributions as Generalizations of FunctionsWhat is a Distribution?The Impulse as the Limit of a SequenceProperties of DistributionsApproximating the ImpulseOther Approximating Sequences and Functions of the ImpulseTest FunctionsConvolutionMultiplication by an Impulse DerivativeThe Dirac-Delta Impulse as a Limit of a Gaussian FunctionFourier Transform of UnityThe Impulse of a FunctionMultiplication by tTime ScalingSome Properties of the Dirac-Delta ImpulseAdditional Fourier TransformsRiemann?Lebesgue LemmaGeneralized LimitsFourier Transform of Higher Impulse DerivativesThe Distribution t?kInitial Derivatives of the TransformThe Unit Step Function as a LimitInverse Fourier Transform and Gibbs PhenomenonRipple EliminationTransforms of |t| and tu(t)The Impulse Train as a LimitSequence of DistributionsPoisson’s Summation FormulaMoving AverageProblemsAnswers to Selected ProblemsGeneralization of Distributions Theory, Extending Laplace-, z- and Fourier-Related TransformsIntroductionAn AnomalyGeneralized Distributions for Continuous-Time FunctionsProperties of the Generalized Impulse in s DomainGeneralized Impulse as a Limit of a Three-Dimensional SequenceDiscrete-Time Domain3-D Test Function as a Possible GeneralizationProperties of the Generalized Impulse in z-DomainAdditional Generalized Impulse PropertiesGeneralized Impulse as Limit of a 3-D SequenceExtended Laplace and z-TransformsGeneralization of Fourier-, Laplace- and z-Related TransformsHilbert Transform GeneralizationGeneralizing the Discrete Hilbert TransformGeneralized Hartley TransformGeneralized Discrete Hartley TransformGeneralization of the Mellin TransformMultidimensional Signals and the Solution of Differential EquationsProblemsAnswers to Selected ProblemsAppendixSymbolsFrequently Needed ExpansionsImportant Trigonometric RelationsOrthogonality RelationsFrequently Encountered FunctionsMathematical FormulaeFrequently Encountered Series SumsBiographies of Pioneering ScientistsPlato (428 BC?347 BC)Euclid (circa 300 BC)Ptolemy (circa 90?168 AD)Abu Jafar Muhammad ibn Musa Al-Khwarizmi (780?850 AD)Nicolaus Copernicus (1473?1543)Galileo Galilei (1564?1642)Sir Isaac Newton (1643?1727)Guillaume-Fran¸cois-Antoine de L’H?opital (1661?1704)Pierre-Simon Laplace (1749?1827)Gaspard Clair Fran¸cois Marie, Baron Riche de Prony (1755?1839)Jean Baptiste Joseph Fourier (1768?1830)Johann Carl Friedrich Gauss (1777?1855)Friedrich Wilhelm Bessel (1784?1846)Augustin-Louis Cauchy (1789?1857)Niels Henrik Abel (1802?1829)Johann Peter Gustav Lejeune Dirichlet (1805?1859)Pafnuty Lvovich Chebyshev (1821?1894)Paul A.M. Dirac