book

Digital Signal Processing: A Practical Guide for Engineers and Scientists

by Steven Smith

October 2013

Intermediate to advanced

672 pages

21h 34m

English

Newnes

Read now

Unlock full access

The Roots of DSPTelecommunicationsAudio ProcessingEcho LocationImage Processing
Signal and Graph TerminologyMean and Standard DeviationSignal vs. Underlying ProcessThe Histogram, Pmf and PdfThe Normal DistributionDigital Noise GenerationPrecision and Accuracy
QuantizationThe Sampling TheoremDigital-to-Analog ConversionAnalog Filters for Data ConversionSelecting the Antialias FilterMultirate Data ConversionSingle-bit Data Conversion

Computer NumbersFixed Point (Integers)Floating Point (Real Numbers)Number PrecisionExecution Speed: Program LanguageExecution Speed: HardwareExecution Speed: Programming Tips
Signals and SystemsRequirements for LinearityStatic Linearity and Sinusoidal FidelityExamples of Linear and Nonlinear SystemsSpecial Properties of LinearitySuperposition: the Foundation of DSPCommon DecompositionsAlternatives to Linearity
The Delta Function and Impulse ResponseConvolutionThe Input Side AlgorithmThe Output Side AlgorithmThe Sum of Weighted Inputs
Common Impulse ResponsesMathematical PropertiesCorrelationSpeed
The Family of Fourier TransformNotation and Format of the Real DFTThe Frequency Domain’s Independent VariableDFT Basis FunctionsSynthesis, Calculating the Inverse DFTAnalysis, Calculating the DFTDualityPolar NotationPolar Nuisances
Spectral Analysis of SignalsFrequency Response of SystemsConvolution via the Frequency Domain
Linearity of the Fourier TransformCharacteristics of the PhasePeriodic Nature of the DFTCompression and Expansion, Multirate methodsMultiplying Signals (Amplitude Modulation)The Discrete Time Fourier TransformParseval’s Relation
Delta Function PairsThe Sinc FunctionOther Transform PairsGibbs EffectHarmoniesChirp Signals
Real DFT Using the Complex DFTHow the FFT WorksFFT ProgramsSpeed and Precision ComparisonsFurther Speed Increases
The Delta FunctionConvolutionThe Fourier TransformThe Fourier Series
Filter BasicsHow Information is Represented in SignalsTime Domain ParametersFrequency Domain ParametersHigh-Pass, Band-Pass and Band-Reject FiltersFilter Classification
Implementation by ConvolutionNoise Reduction vs. Step ResponseFrequency ResponseRelatives of the Moving Average FilterRecursive Implementation
Strategy of the Windowed-SincDesigning the FilterExamples of Windowed-Sinc FiltersPushing it to the Limit
Arbitrary Frequency ResponseDeconvolutionOptimal Filters
The Overlap-Add MethodFFT ConvolutionSpeed Improvements
The Recursive MethodSingle Pole Recursive FiltersNarrow-band FiltersPhase ResponseUsing Integers
The Chebyshev and Butterworth ResponsesDesigning the FilterStep Response OvershootStability
Match #1: Analog vs. Digital FiltersMatch #2: Windowed-Sinc vs. ChebyshevMatch #3: Moving Average vs. Single Pole
Human HearingTimbreSound Quality vs. Data RateHigh Fidelity AudioCompandingSpeech Synthesis and RecognitionNonlinear Audio Processing
Digital Image StructureCameras and EyesTelevision Video SignalsOther Image Acquisition and DisplayBrightness and Contrast AdjustmentsGrayscale TransformsWarping
Convolution3 × 3 Edge ModificationConvolution by SeparabilityExample of a Large PSF: Illumination FlatteningFourier Image AnalysisFFT ConvolutionA Closer Look at Image Convolution
Spatial ResolutionSample Spacing and Sampling ApertureSignal-to-Noise RatioMorphological Image ProcessingComputed Tomography
Target DetectionNeural Network ArchitectureWhy Does It Work?Training the Neural NetworkEvaluating the ResultsRecursive Filter Design
Run-Length EncodingHuffman EncodingDelta EncodingLZW CompressionJPEG (Transform Compression)MPEG
How DSPs Are Different from Other MicroprocessorsCircular BufferingArchitecture of the Digital Signal ProcessorFixed versus Floating PointC versus AssemblyHow Fast Are DSPs?The Digital Signal Processor Market
The ADSP-2106x familyThe SHARC EZ-KIT LiteDesign Example: An FIR Audio FilterAnalog measurements on a DSP systemAnother Look at Fixed versus Floating PointAdvanced Software Tools
The Complex Number SystemPolar NotationUsing Complex Numbers by SubstitutionComplex Representation of SinusoidsComplex Representation of SystemsElectrical Circuit Analysis
The Real DFTMathematical EquivalenceThe Complex DFTThe Family of Fourier TransformsWhy the Complex Fourier Transform Is Used
The Nature of the s-DomainStrategy of the Laplace TransformAnalysis of Electric CircuitsThe Importance of Poles and ZerosFilter Design in the s-Domain
The Nature of the z-DomainAnalysis of Recursive SystemsCascade and Parallel StagesSpectral InversionGain ChangesChebyshev-Butterworth Filter DesignThe Best and Worst of DSP

Content preview from Digital Signal Processing: A Practical Guide for Engineers and Scientists

CHAPTER 11

Fourier Transform Pairs

For every time domain waveform there is a corresponding frequency domain waveform, and vice versa. For example, a rectangular pulse in the time domain coincides with a sinc function [i.e., sin(x)/x] in the frequency domain. Duality provides that the reverse is also true; a rectangular pulse in the frequency domain matches a sinc function in the time domain. Waveforms that correspond to each other in this manner are called Fourier transform pairs. Several common pairs are presented in this chapter.

Delta Function Pairs

For discrete signals, the delta function is a simple waveform, and has an equally simple Fourier transform pair. Figure 11-1a shows a delta function in the time domain, with its frequency ...