onvolution1Introduction
1-1MathematicalRepresentationofSignals
1-2MathematicalRepresentationofSystems
1-3ThinkingAboutSystems
1-4TheNextStep
2Sinusoids
2-1TuningForkExperiment
2-2ReviewofSineandCosineFunctions
2-3SinusoidalSignals.2-3.1RelationofFrequencytoPeriod
2-3.2PhaseShiftandTimeShift
2-4SamplingandPlottingSinusoids
2-5ComplexExponentialsandPhasors
2-5,1ReviewofComplexNumbers
2-5.2ComplexExponentialSignals
2-5.3TheRotatingPhasorInterpretation
2-5.4InverseEulerFormulas
2-6PhasorAddition.
2-6.1AdditionofComplexNumbers
2-6.2PhasorAdditionRule
2-6.3PhasorAdditionRule:Example
2-6.4MATLABDemoofPhasors
2-6.5SummaryofthePhasorAdditionRule
2-7PhysicsoftheTuningFork
2-7.1EquationsfromLawsofPhysics
2-7.2GeneralSolutiontotheDifferentialEquation
2-7.3ListeningtoTones
2-8TimeSignals:MoreThanFormulas
2-9SummaryandLinks
2-10Problems
3SpectrumRepresentation
3-1TheSpectrumofaSumofSinusoids
3-1.1NotationChange
3-1.2GraphicalPlotoftheSpectrum
3-2BeatNotes
3-2.1MultiplicationofSinusoids
3-2.2BeatNoteWaveform
3-2.3AmplitudeModulation
3-3PeriodicWaveforms
3-3.1SyntheticVowel
3-3.2ExampleofaNonperiodicSignal
3-4FourierSeries
3-4.1FourierSeries:Analysis
3-4.2FourierSeriesDerivation
3-5SpectrumoftheFourierSeries.FourierAnalysisofPeriodicSignals
3-6.1TheSquareWave
3-6.1.1DCValueofaSquareWave
3-6.2SpectrumforaSquareWave
3-6.3SynthesisofaSquareWave
3-6.4TriangleWave
3-6.5SynthesisofaTriangleWave
3-6.6ConvergenceofFourierSynthesis
3-7Time-FrequencySpectrum
3-7.1SteppedFrequency
3-7.2SpectrogramAnalysis
3-8FrequencyModulation:ChirpSignals
3-8.1ChirporLinearlySweptFrequency
3-8.2ACloserLookatInstantaneousFrequency
3-9SummaryandLinks
3-10Problems
4SamplingandAliasing
4-1Sampling.
4-1.1SamplingSinusoidalSignals
4-1.2TheConceptofAliasing.
4-1.3SpectrumofaDiscrete-TimeSignal.
4-1.4TheSamplingTheorem
4-1.5IdealReconstruction.
4-2SpectrumViewofSamplingandReconstruction
4-2.1SpectrumofaDiscrete-TimeSignalObtainedbySampling
4-2.2Over-Sampling.
4-2.3AliasingDuetoUnder-Sampling
4-2.4FoldingDuetoUnder-Sampling
4-2.5MaximumReconstructedFrequency
4-3StrobeDemonstration
4-3.1SpectrumInterpretation
4-4Discrete-to-ContinuousConversion
4-4.1InterpolationwithPulses.
4-4.2Zero-OrderHoldInterpolation.
4-4.3LinearInterpolation4-4.4CubicSplineInterpolation
4-4.5Over-SamplingAidsInterpolation.
4-4.6IdealBandlimitedInterpolation
4-5TheSamplingTheorem
4-6SummaryandLinks
4-7Problems
5FIRFilters
5-1Discrete-TimeSystems
5-2TheRunning-AverageFilter
5-3TheGeneralFIRFilter
5-3.1AnIllustrationofFIRFiltering
5-3.2TheUnitImpulseResponse
5-3.2.1UnitImpulseSequence
5-3.2.2UnitImpulseResponseSequence
5-3.2.3TheUnit-DelaySystem
5-3.3ConvolutionandFIRFilters
5-3.3.1ComputingtheOutputofaConvolution
5-3.3.2ConvolutioninMATLAB
5-4ImplementationofFIRFilters
5-4.1BuildingBlocks
5-4.1.1Multiplier
5-4.1.2Adder
5-4.1.3UnitDelayi
5-4.2BlockDiagrams
5-4.2.1OtherBlockDiagrams
5-4.2.2InternalHardwareDetails
5-5LinearTime-invariant(LTI)Systems
5-5.1TimeInvariance
5-5.2Linearity
5-5.3TheFIRCase
5-6ConvolutionandLTISystems
5-6.1DerivationoftheConvolutionSum
5-6.2SomePropertiesofLTlSystems
5-6.2.1ConvolutionasanOperator
5-6.2.2CommutativePropertyofConvolution
5-6.2.3AssociativePropertyofConvolution
5-7CascadedLTlSystems
5-8ExampleofFIRFiltering
5-9SummaryandLinks
5-10Problems
6FrequencyResponseofFIRFilters
6-1SinusoidalResponseofFIRSystems
6-2SuperpositionandtheFrequencyResponse
6-3Steady-StateandTransientResponse
6-4PropertiesoftheFrequencyResponse
6-4.1RelationtoImpulseResponseandDifferenceEquation
6-4.2PeriodicityofH
6-4.3ConjugateSymmetry
6-5GraphicalRepresentationoftheFrequencyResponse
6-5.1DelaySystem
6-5.2First-DifferenceSystem
6-5.3ASimpleLowpassFilter
6-6CascadedLTISystems
6-7Running-AverageFiltering
6-7.1PlottingtheFrequencyResponse
6-7.2CascadeofMagnitudeandPhase
6-7.3Experiment:SmoothinganImage
6-8FilteringSampledContinuous-TimeSignals
6-8.1Example:LowpassAverager
6-8.2InterpretationofDelay
6-9SummaryandLinks
6-10Problems
7z-Transforms
7-1Definitionofthez-Transform
7~2Thez-TransformandLinearSystems
7-2.1Thez-TransformofanFIRFilter
Propertiesofthez-Transform
7-3.1TheSuperpositionPropertyofthez-Transform
7-3.2TheTime-DelayPropertyofthez-Transform.
7-3.3AGeneralz-TransformFormula
7-4Thez-TransformasanOperator
7-4.1Unit-DelayOperator
7-4.2OperatorNotation
7-4.3OperatorNotationinBlockDiagrams
7-5Convolutionandthez-Transform.
7-5.1CascadingSystems
7-5.2Factoringz-Polynomials
7-5.3Deconvolution
7-6RelationshipBetweenthez-Domainandthec3-Domain
7-6.1Thez-PlaneandtheUnitCircle
7-6.2TheZerosandPolesofH(z)
7-6.3SignificanceoftheZerosofH(z).
7-6.4NullingFilters
7-6.5GraphicalRelationBetweenzandcb
7-7UsefulFilters
7-7.1TheL-PointRunning-SumFilter
7-7.2AComplexBandpassFilter
7-7.3ABandpassFilterwithRealCoefficients
7-8PracticalBandpassFilterDesign
7-9PropertiesofLinear-PhaseFilters
7-9.1TheLinear-PhaseCondition
7-9.2LocationsoftheZerosofFIRLinear-PhaseSystems
7-10SummaryandLinks
7-11Problems
8IIRFilters
8-1TheGeneralIIRDifferenceEquation
8-2Time-DomainResponse
8-2.1LinearityandTimeInvarianceofIIRFilters
8-2.2ImpulseResponseofaFirst-OrderIIRSystem.
8-2.3ResponsetoFinite-LengthInputs
8-2.4StepResponseofaFirst-OrderRecursiveSystem.
8-3SystemFunctionofanIIRFilter
8-3.1TheGeneralFirst-OrderCase
8-3.2TheSystemFunctionandBlock-DiagramStructures
8-3.2.1DirectFormIStructure
8-3.2.2DirectFormIIStructure
8-3.2.3TheTransposedFormStructure
8-3.3RelationtotheImpulseResponse
8-3.4SummaryoftheMethod
8-4PolesandZeros
8-4.1PolesorZerosattheOriginorInfinity
8-4.2PoleLocationsandStability
8-5FrequencyResponseofanIIRFilter
8-5.1FrequencyResponseusingMATLAB
8-5.2Three-DimensionalPlotofaSystemFunction.
8-6ThreeDomains
8-7TheInversez-TransformandSomeApplications
8-7.1RevisitingtheStepResponseofaFirst-OrderSystem
8-7.2AGeneralProcedureforInversez-Transformation
8-8Steady-StateResponseandStability
8-9Second-OrderFilters
8-9.1z-TransformofSecond-OrderFilters
8-9.2StructuresforSecond-OrderIIRSystems
8-9.3PolesandZeros
8-9.4ImpulseResponseofaSecond-OrderIIRSystem
8-9.4.1RealPoles
8-9.5ComplexPoles
8-10FrequencyResponseofSecond-OrderIIRFilter
8-10.1FrequencyResponseviaMATLAB
8-10.23-dBBandwidth.
8-10.3Three-DimensionalPlotofSystemFunctions
8-11ExampleofanIIRLowpassFilter
8-12SummaryandLinks
8-13Problems
9Continuous-TimeSignalsandLTISystems
9-1Continuous-TimeSignals
9-1.1Two-SidedInfinite-LengthSignals
9-1.2One-SidedSignals
9-1.3Finite-LengthSignals
9-2TheUnitImpulse
9-2.1SamplingPropertyoftheImpulse
9-2.2MathematicalRigor
9-2.3EngineeringReality
9-2.4DerivativeoftheUnitStep
9-3Continuous-TimeSystems
9-3.1SomeBasicContinuous-TimeSystems
9-3.2Continuous-TimeOutputs
9-3.3AnalogousDiscrete-TimeSystems
9-4LinearTime-InvariantSystems
9-4.1Time-Invariance
9-4.2Linearity
9-4.3TheConvolutionIntegral
9-4,4PropertiesofConvolution
9-5ImpulseResponsesofBasicLTISystems
9-5.1Integrator.
9-5.2Differentiator
9-5.3IdealDelay
9-6ConvolutionofImpulses
9-7EvaluatingConvolutionIntegrals
9-7.1DelayedUnit-StepInput
9-7.2EvaluationofDiscreteConvolution
9-7.3Square-PulseInput
9-7.4VeryNarrowSquarePulseInput
9-7.5DiscussionofConvolutionExamples
9-8PropertiesofLTISystems
9-8.1CascadeandParallelCombinations
9-8.2DifferentiationandIntegrationofConvolution
9-8.3StabilityandCausality
9-9UsingConvolutiontoRemoveMulfipathDistortion.
9-10Summary
9-11Problems
10FrequencyResponse
10-1TheFrequencyResponseFunctionforLTISystems.
10-1.1PlottingtheFrequencyResponse.
10-1.1.1LogarithmicPlot.
10-1.2MagnitudeandPhaseChangesResponsetoRealSinusoidalSignals
10-2.1CosineInputs
10-2.2SymmetryofH(jw)
10-2.3ResponsetoaGeneralSumofSinusoids
10-2.4PeriodicInputSignals
10-3IdealFilters
10-3.1IdealDelaySystem
10-3.2IdealLowpassFilter
10-3.3IdealHighpassFilter
10-3.4IdealBandpassFilter
10-4ApplicationofIdealFilters
10-5Time-DomainorFrequency-Domain?
10-6Summary/Future
10-7Problems
Continuous-TimeFourierTransform
11-1DefinitionoftheFourierTransform.
11-2FourierTransformandtheSpectrum.
11-2.1LimitoftheFourierSeries
11-3ExistenceandConvergenceoftheFourierTransform
11-4ExamplesofFourierTransformPairs
!1-4.1Right-SidedRealExponentialSignals
11-4.1.1BandwidthfindDecayRate
11-4.2RectangularPulseSignals
11-4.3BandlimitedSignals
11-4.4ImpulseinTimeorFrequency
11-4.5Sinusoids
11-4.6PeriodicSignals
11-5PropertiesofFourierTransformPairs
11-5.1TheScalingProperty
11-5.2SymmetryPropertiesofFourierTransformPairs
11-6TheConvolutionProperty
11-6.1FrequencyResponse
11-6.2FourierTransformofaConvolution
11-6.3ExamplesoftheUseoftheConvolutionProperty
11-6.3.1ConvolutionofTwoBandlimitedFunctions
11-6.3.2ProductofTwoSincFunctions
11-6.3.3PartialFractionExpansions
11-7BasicLTISystems
11-7.1TimeDelay
11-7.2Differentiation
11-7.3SystemsDescribedbyDifferentialEquations
11-8TheMultiplicationProperty
11-8.1TheGeneralSignalMultiplicationProperty
11-8.2TheFrequencyShiftingProperty
1I-9TableofFourierTransformPropertiesandPairs
11-10UsingtheFourierTransformforMultipathAnalysis
11-11Summary
11-12Problems
12Filtering,Modulation,andSampling
12-1LinearTime-InvariantSystems
12-1.1CascadeandParallelConfigurations
12-1.2IdealDelay
12-1.3FrequencySelectiveFilters
12-1.3.1IdealLowpassFilter
12-1.3.2OtherIdealFrequencySelectiveFilters
12-1.4ExampleofFilteringintheFrequency-Domain
12-1.5CompensationfortheEffectofanLTIFilter
12-2SinewaveAmplitudeModulation
12-2.1Double-SidebandAmplitudeModulation
12-2.2DSBAMwithTransmittedCarrier(DSBAM-TC)
12-2.3FrequencyDivisionMultiplexing
12-3SamplingandReconstruction
12-3.1TheSamplingTheoremandAliasing
12-3.2BandlimitedSignalReconstruction
12-3.3BandlimitedInterpolation
12-3.4IdealC-to-DandD-to-CConverters
12-3.5TheDiscrete-TimeFourierTransform
12-3.6TheInverseDTFY
12-3.7Discrete-TimeFilteringofContinuous-TimeSignals
12-4Summary
12-5Problems
ComputingtheSpectrum
13-1FiniteFourierSum.
13-2TooManyFourierTransforms?
13-2.1RelationoftheDTFTtotheCTFT
13-2.2RelationoftheDPTtotheDTFT
13-2.3RelationoftheDPTtotheCTFT
13-3Time-Windowing
13-4AnalysisofaSumofSinusoids
13-4.1DTPTofaWindowedSinusoid
13-5DiscreteFourierTransform
13-5.1TheInverseDPT
13-5.2SummaryoftheDFTRepresentation.
13-5.3TheFastFourierTransform(FFT)
13-5.4NegativeFrequenciesandtheDFT
13-5.5DFTExample
13-6SpectrumAnalysisofFinite-LengthSignals
13-7SpectrumAnalysisofPeriodicSignals
13-8TheSpectrogram
13-8.1SpectrogramDisplay
13-8.2SpectrogramsinMATLAB
13-8.3SpectrogramofaSampledPeriodicSignal
13-8.4ResolutionoftheSpectrogram
13-8.4.1ResolutionExperiment
13-8.5SpectrogramofaMusicalScale
13-8.6SpectrogramofaSpeechSignal
13-8.7FilteredSpeech
13-9TheFastFourierTransform(FFT)
13-9.1DerivationoftheFFT
13-9.1.1FFrOperationCount
13-10SummaryandLinks
13-11Problems
AComplexNumbers
A-1Introduction.
A-2NotationforComplexNumbers
A-2.1RectangularFormA-2.2PolarForm
A-2.3Conversion:RectangularandPolar
A-2.4DifficultyinSecondorThirdQuadrant
A-3Euler'sFormula
A-3.1InverseEulerFormulas
A-4AlgebraicRulesforComplexNumbers
A-4.1ComplexNumberExercises
A-5GeometricViewsofComplexOperations
A-5.1GeometricViewofAddition
A-5.2GeometricViewofSubtraction
A-5.3GeometricViewofMultiplication
A-5.4GeometricViewofDivision
A-5.5GeometricViewoftheInverse,z-1
A-5.6GeometricViewoftheConjugate
A-6PowersandRoots
A-6.1RootsofUnity
A-6.1.1ProcedureforFindingMultipleRoots
A-7SummaryandLinks
A-8Problems
BProgramminginMATLAB
B-1MATLABHelp
B-2MatrixOperationsandVariables
B-2.1TheColonOperator
B-2.2MatrixandArrayOperations
B-2.2.1AReviewofMatrixMultiplication.
B-2.2.2PointwiseArrayOperations
B-3PlotsandGraphics
B-3.1FigureWindows
B-3.2MultiplePlots
B-3.3PrintingandSavingGraphics
B-4ProgrammingConstructs
B-4.1MATLABBuilt-inFunctions
B-4.2ProgramFlow
B-5MATLABScriptsWritingaMATLABFunction
B-6.1CreatingAClipFunction
B-6.2DebuggingaMATLABM-file
B-7ProgrammingTips
B-7.1AvoidingLoops
B-7.2RepeatingRowsorColumns
B-7.3VectorizingLogicalOperations
B-7.4CreatinganImpulse
B-7.5TheFindFunction
B-7.6SeektoVectorize
B-7.7ProgrammingStyle
CLaboratoryProjects
C-1IntroductiontoMATLAB
C-I.1Pre-Lab
C-I.I.1Overview
C-1.1.2Movies:MATLABTutorials
C-1.1.3GettingStarted
C-1.2Warm-up
C-1.2.1MATLABArrayIndexing
C-1.2.2MATLABScriptFiles
C-1.2.3MATLABSound(optional)
C-1.3Laboratory:ManipulatingSinusoidswithMATLAB
C-1.3.1TheoreticalCalculations
C-1.3.2ComplexAmplitude
C-1.4LabReviewQuestions
C-2EncodingandDecodingTouch-ToneSignals
C-2.1Introduction
C-2.1.1Review
C-2.1.2Background:TelephoneTouch-ToneDialing
C-2.1.3DTMFDecoding
C-2.2Pre-Lab
C-2.2.1SignalConcatenation
C-2.2.2CommentonEfficiency
C-2.2.3EncodingfromaTable
C-2.2.4OverlayPlotting
C-2.3Warm-up:DTMFSynthesis
C-2.3.1DTMFDialFunction
C-2.3.2SimpleBandpassFilterDesign
C-2.4Lab:DTMFDecoding
C-2.4.1FilterBankDesign:dtmfdesign.m
C-2.4.2AScoringFunction:dtmfscore.m
C-2.4.3DTMFDecodeFunction:dtmfrun,m
C-2.4.4Testing
C-2.4.5TelephoneNumbers
C-2.4.6Demo
C-3TWoConvolutionGUIs
C-3.1Introduction
C-3.2Pre-Lab:RuntheGUIs
C-3.2.1Discrete-TimeConvolutionDemo
C-3.2.2Continuous-TimeConvolutionDemo
C-3.3Warm-up:RuntheGUIs
C-3.3.1Continuous-TimeConvolutionGUI
C-3.3.2DiscreteConvolutionGUI
C-3.4LabExercises
C-3.4.1Continuous-TimeConvolution
C-3.4.2Continuous-TimeConvolutionAgain
C-3.4.3Discrete-TimeConvolution
鄂公网安备 42010302001612号 