Multirate Signal Processing for Com Sys

618 Pages·2021·26.636 MB·English

by  Harris

MULTIRATE SIGNAL PROCESSING River Publishers Series in Signal, Image, and Speech Processing
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FOR COMMUNICATION SYSTEMS OIR
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Second Edition

US FOR COMMUNICATION SYSTEMS
fredric j harris I
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Multirate Signal processing can improve system performance and reduce costs AA
Second Edition
in applications ranging from laboratory instruments, cable modems, wireless TL
systems, satellites, Radar, Sonar, and consumer entertainment products. This IO P
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second edition continues to offer a systematic, clear, and intuitive introduction N
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to multirate signal processing for working engineers and system designers.
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Significant new material and fresh concepts, including Green Signal Processing YE
techniques have been introduced. SS
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The author uses extensive examples and figures to illustrate a wide EI
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range of multirate techniques, from basic resampling to leading-edge cascade
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and multi-stage filter structures. Along the way he draws on extensive research

and consulting experience to introduce processing “tricks” shown to maximize
performance and efficiency. Coverage includes:
• Effect of sampling and resampling in time and frequency domains
• R elationships between FIR filter specifications and filter length (# of
taps)
• Window design and equal-ripple (Remez) design techniques
• S quare-Root Nyquist and Half-band Filters including new
f
enhancements r
e
• Polyphase FIR filters: up-sampling, down-sampling
d
• P olyphase M-path analysis and synthesis channelizers and cascade
r
pairs i
c
• Polyphase interpolators for arbitrary sample rate changes

• Dyadic half-band filters, quadrature mirror filters j

• Channel banks for multiple arbitrary bandwidths and center frequencies h
• C omprehensive coverage of recursive all-pass filters and channelizers, a
non-uniform and uniform phase, mixed recursive and non-recursive r
r
• Comparisons with traditional DSP designs
i
• Extensive applications coverage throughout s
fredric j harris
River Publishers
River
River Publishers
Multirate Signal Processing for
Communication Systems
Second Edition
RIVER PUBLISHERS SERIES IN SIGNAL,
IMAGE AND SPEECH PROCESSING
SeriesEditors:
MARCELOSAMPAIODEALENCAR
UniversidadeFederaldaBahiaUFBA,Brasil
MONCEFGABBOUJ
TampereUniversityofTechnology,Finland
THANOSSTOURAITIS
UniversityofPatras,Greece
and
KhalifaUniversity,UAE
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The “River Publishers Series in Signal, Image and Speech Processing” is a series of
comprehensiveacademicandprofessionalbookswhichfocusonallaspectsofthetheoryand
practice of signal processing. Books published in the series include research monographs,
edited volumes, handbooks and textbooks. The books provide professionals, researchers,
educators,andadvancedstudentsinthefieldwithaninvaluableinsightintothelatestresearch
anddevelopments.
Topicscoveredintheseriesinclude,butarebynomeansrestrictedtothefollowing:
• SignalProcessingSystems
• DigitalSignalProcessing
• ImageProcessing
• SignalTheory
• StochasticProcesses
• DetectionandEstimation
• PatternRecognition
• OpticalSignalProcessing
• Multi-dimensionalSignalProcessing
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• BiomedicalSignalProcessing
• AcousticandVibrationSignalProcessing
• DataProcessing
• RemoteSensing
• SignalProcessingTechnology
• SpeechProcessing
• RadarSignalProcessing
Foralistofotherbooksinthisseries,visitwww.riverpublishers.com
Multirate Signal Processing for
Communication Systems
Second Edition
fredric j harris
UniversityofCaliforniaSanDiego,USA
River Publishers
Published,soldanddistributedby:
RiverPublishers
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www.riverpublishers.com
ISBN:978-87-7022-210-5(Hardback)
978-87-7022-209-9(Ebook)
©2021RiverPublishers
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedin
aretrievalsystem,ortransmittedinanyformorbyanymeans,mechanical,
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thepublishers.
Tothememoryofmyparents,
EdithandSeymourHarris,
MyWife,Penelope,
Ourchildren,DanielleandRobyn,
Ourgrandson,Justin,
Andtoallmystudentsandcolleagues
withwhomIsharethejoyoflearning.
“Alittlelearningisadangerousthing;
drinkdeep,ortastenotthePierianspring:
thereshallowdraughtsintoxicatethebrain,
anddrinkinglargelysobersusagain.”
AlexanderPope(1688–1744)
AnEssayonCriticism
Contents
Preface xiii
ListofFigures xxi
ListofTables lv
ListofAbbreviations lvii
1 WhyMultirateFilters? 1
1.1 CompactDisc4-to-1Oversample . . . . . . . . . . . . . . 2
1.2 Anti-AliasFiltering . . . . . . . . . . . . . . . . . . . . . . 7
2 TheResamplingProcess 13
2.1 TheSamplingSequence . . . . . . . . . . . . . . . . . . . 15
2.1.1 ModulationDescriptionofResampledSequence . . 19
2.2 WhatIsaMultirateFilter? . . . . . . . . . . . . . . . . . . 20
2.2.1 PropertiesofResamplers . . . . . . . . . . . . . . . 23
2.2.2 ExamplesofResamplingFilters . . . . . . . . . . . 26
2.3 UsefulPerspectivesforMultirateFilters . . . . . . . . . . . 29
2.4 NyquistandtheSamplingProcess . . . . . . . . . . . . . . 33
3 DigitalFilters 41
3.1 FilterSpecifications . . . . . . . . . . . . . . . . . . . . . . 42
3.2 Windowing . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 TheRemez-FirpmAlgorithm . . . . . . . . . . . . . . . . . 55
3.3.1 Equiripplevs.1/f RippleDesigns . . . . . . . . . . 64
3.3.2 AcceptableIn-BandRippleLevels . . . . . . . . . . 71
4 UsefulClassesofFilters 87
4.1 NyquistFilterandSquare-RootNyquistFilter . . . . . . . . 88
4.2 TheCommunicationPath . . . . . . . . . . . . . . . . . . . 91
vii
viii Contents
4.3 TheSampledCosineTaper . . . . . . . . . . . . . . . . . . 95
4.3.1 RootRaisedCosineSide-LobeLevels . . . . . . . . 97
4.3.2 ImprovingtheStop-BandAttenuation . . . . . . . . 99
4.4 Half-BandFilters . . . . . . . . . . . . . . . . . . . . . . . 106
5 SystemsThatUseResamplingFilters 117
5.1 FilteringWithLargeRatioofSampleRatetoBandwidth . . 117
5.1.1 PartialSumAccumulator:TheDualForm . . . . . . 121
5.1.2 GenerateBasebandNarrowbandNoise . . . . . . . 126
5.1.3 GenerateNarrowbandNoiseataCarrierFrequency . 129
5.2 WorkloadofMultirateFilter . . . . . . . . . . . . . . . . . 131
6 PolyphaseFIRFilters 139
6.1 Channelizer . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.1.1 TransformingtheBand-PassFilter . . . . . . . . . . 146
6.2 SeparatingtheAliases. . . . . . . . . . . . . . . . . . . . . 155
6.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7 ResamplingFilters 167
7.1 Interpolators . . . . . . . . . . . . . . . . . . . . . . . . . . 168
7.1.1 Simple1-to-MInterpolator . . . . . . . . . . . . . . 168
7.2 InterpolatorArchitecture . . . . . . . . . . . . . . . . . . . 174
7.2.1 PolyphasePartition . . . . . . . . . . . . . . . . . . 175
7.3 Band-PassInterpolator . . . . . . . . . . . . . . . . . . . . 178
7.4 RationalRatioResampling . . . . . . . . . . . . . . . . . . 182
7.5 ArbitraryResamplingRatio . . . . . . . . . . . . . . . . . . 185
7.5.1 NearestLeftNeighborInterpolation . . . . . . . . . 186
7.5.2 Two-NeighborInterpolation . . . . . . . . . . . . . 196
7.6 FarrowFilter . . . . . . . . . . . . . . . . . . . . . . . . . 200
7.6.1 ClassicalInterpolator . . . . . . . . . . . . . . . . . 200
7.6.2 PolynomialApproximation . . . . . . . . . . . . . . 205
7.6.3 FarrowStructure . . . . . . . . . . . . . . . . . . . 208
8 Half-BandFilters 219
8.1 Half-BandLow-PassFilters. . . . . . . . . . . . . . . . . . 220
8.2 Half-BandHigh-PassFilter . . . . . . . . . . . . . . . . . . 221
8.3 WindowDesignofHalf-BandFilter . . . . . . . . . . . . . 223
8.4 Firpm-RemezAlgorithmDesignofHalf-BandFilters . . . . 224
8.4.1 Half-BandFirpmAlgorithmDesignTrick . . . . . . 225
Contents ix
8.5 HilbertTransformBand-PassFilter . . . . . . . . . . . . . . 227
8.5.1 ApplyingtheHilbertTransformFilter . . . . . . . . 228
8.6 InterpolatingWithLow-PassHalf-BandFilters . . . . . . . 231
8.7 DyadicHalf-BandFilters . . . . . . . . . . . . . . . . . . . 234
9 PolyphaseChannelizers 241
9.1 AnalysisChannelBank . . . . . . . . . . . . . . . . . . . . 242
9.2 ArbitraryOutputSampleRates . . . . . . . . . . . . . . . . 245
9.2.1 NobleIdentityBasedAnalysisFilterBank . . . . . 257
9.3 NobleIdentityBasedSynthesisFilterBank . . . . . . . . . 268
10 CascadeChannelizers 275
10.1 PerfectReconstructionAnalysis–SynthesisFilterBanks . . . 276
10.2 CascadeAnalysisandSynthesisChannelizers . . . . . . . . 282
10.2.1 CascadeChannelizerswithChannelMasks . . . . . 284
10.2.2 Compare Cascade Channelizers to Direct
ImplementationFIR . . . . . . . . . . . . . . . . . 289
10.3 EnhancedCapabilitiesofCoupledChannelizers . . . . . . . 293
10.3.1 IFFTCenteredChannelizerEnhancements . . . . . 296
10.4 MultipleBandwidthsArbitraryFrequencyCenter
Channelizers . . . . . . . . . . . . . . . . . . . . . . . . . 302
10.5 ChannelizerswithEvenandOddIndexedBinCenters . . . . 309
11 RecursivePolyphaseFilters 323
11.1 All-PassRecursiveFilters . . . . . . . . . . . . . . . . . . . 324
11.1.1 PropertiesofAll-PassFilters . . . . . . . . . . . . . 326
11.1.2 ImplementingFirst-OrderAll-PassNetworks . . . . 332
11.2 Two-PathAll-PassRecursiveFilters . . . . . . . . . . . . . 337
11.2.1 Two-PathHalf-BandFilters:Non-UniformPhase . . 338
11.2.2 Two-PathHalf-BandFilters:LinearPhase . . . . . . 347
11.3 Comparison of Non-Uniform and Equal Ripple Phase Two-
PathFilters . . . . . . . . . . . . . . . . . . . . . . . . . . 350
11.4 Pass-BandandStop-BandResponseinHalf-BandFilters . . 355
11.5 TransformingHalf-BandtoArbitrary-Bandwidth . . . . . . 357
11.5.1 Low-PasstoLow-PassTransformation . . . . . . . 357
11.5.2 Low-PasstoBand-PassTransformation . . . . . . . 361
11.6 MultirateConsiderationsofRecursiveHalf-BandFilters . . 367
11.7 Hilbert-TransformFilterVariantofTwo-PathAll-PassFilter 376
11.8 M-PathRecursiveAll-PassFilters . . . . . . . . . . . . . . 380