信号处理引论：英文本

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