Multirate systems and filter banks:
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Delhi
Dorling Kindersley
2006
|
Ausgabe: | 1. impr. |
Schriftenreihe: | Prentice Hall signal processing series
|
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | Literaturverz. S. 869 - 887 |
Beschreibung: | XVI, 911 S. graph. Darst. |
ISBN: | 8177589423 |
Internformat
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adam_text | Titel: Multirate systems and filter banks
Autor: Vaidyanathan, P. P
Jahr: 2006
Contents
Preface xi
PART 1 INTRODUCTORY CHAPTERS
1 Introduction 1
1.1 Major Developments 3
1.2 Scope andOutline 8
2 Review of Discrete-Time Systems 12
2.0 Introduction 12
2.1 Discrete-Time Signals 12
2.2 Multi-Input Multi-Output Systems 24
2.3 Notations 28
2.4 Discrete-Time Filters (Digital Filters) 31
Problems 39
3 Review of Digital Filters 42
3.0 Introduction 42
3.1 Filter Design Specifications 42
3.2 FIR Filter Design 45
3.3 IIR Filter Design 60
3.4 Ailpass Filters 71
3.5 Special Types of Filters 83
3.6 IIR Filters Based on Two Ailpass Filters 84
3.7 Concluding Remarks 91
Problems 93
4 Fundamentals of Multirate Systems 100
4.0 Introduction 100
4.1 Basic Multirate Operations 100
4.2 Interconnection of Building Blocks 118
4.3 The Polyphase Representation 120
4.4 Multistage Implementations 134
4.5 Some Applications of Multirate Systems 143
4.6 Special Filters and Filter Banks 151
4.7 Multigrid Methods 168
Problems 178
PART 2 MULTIRATE FILTER BANKS
5 Maximally Decimated Filter Banks 188
5.0 Introduction 188
5.1 Errors Created in the QMF Bank 191
5.2 A Simple Alias-Free QMF System 196
5.3 Power Symmetric QMF Banks 204
5.4 M-channel Filter Banks 223
5.5 Polyphase Representation 230
5.6 Perfect Reconstruction (PR) Systems 234
5.7 Alias-Free Filter Banks 245
5.8 Tree Structured Filter Banks 254
5.9 Transmultiplexers 259
5.10 Summary and Tables 266
Problems 272
6 Paraunitary Perfect Reconstruction (PR) Filter Banks 286
6.0 Introduction 286
6.1 Lossless Transfer Matrices 288
6.2 Filter Bank Properties Induced by Paraunitariness 294
6.3 Two Channel FIR Paraunitary QMF Banks 298
6.4 The Two Channel Paraunitary QMF Lattice 302
6.5 A/-channeI FIR Paraunitary Filter Banks 314
6.6 TVansform Coding and the LOT 322
6.7 Summary, Comparisons, and Tables 326
Problems 333
7 Linear Phase Perfect Reconstruction QMF Banks 337
7.0 Introduction 337
7.1 Some Necessary Conditions 337
7.2 Lattice Structures for Linear Phase FIR PR QMF Banks 339
7.3 Formal Synthesis of Linear Phase FIR PR QMF Lattice 347
Problems 351
8 Cosine Modulated Filter Banks 353
8.0 Introduction 353
8.1 The Pseudo QMF Bank 354
8.2 Design of the Pseudo QMF Bank 363
8.3 Efficient Polyphase Structures 370
8.4 Deeper Properties of Cosine Matrices 373
8.5 Cosine Modulated Perfect Reconstruction Systems 377
Problems 392
PART 3 SPECIAL TOPICS
9 Quantization Effects 394
9.0 Introduction 394
9.1 Types of Quantization Effects 394
9.2 Review of Standard Techniques 397
viii Contents
9.3 Noise Transmission in Multirate Systems 405
9.4 Noise in Filter Banks 408
9.5 Filter Bank Output Noise 412
9.6 Limit Cycles 416
9.7 Coefficient Quantization 418
Problems 424
10 Multirate Filter Bank Theory and Related Topics 427
10.0 Introduction 427
10.1 Block Filters, LPTV Systems and Multirate Filter Banks 427
10.2 Unconventional Sampling Theorems 436
Problems 454
11 The Wavelet Transform and its Relation to Multirate Filter Banks 457
11.0 Introduction 457
11.1 Background and Outline 458
11.2 The Short-Time Fourier Transform 463
11.3 The Wavelet Transform 481
11.4 Discrete-Time Orthonormal Wavelets 500
11.5 Continuous-Time Orthonormal Wavelet Basis 510
11.6 Concluding Remarks 536
Problems 539
12 Multidimensional Multirate Systems 545
12.0 Introduction 545
12.1 Multidimensional Signals 546
12.2 Sampling a Multidimensional Signal 555
12.3 Minimum Sampling Density 568
12.4 Multirate Fundamentals 572
.12.5 Alias-Free Decimation 597
12.6 Cascade Connections 603
12.7 Multirate Filter Design 608
12.8 Special Filters and Filter Banks 623
12.9 Maximally Decimated Filter Banks 627
12.10 Concluding Remarks 641
Problems 650
PART 4 MULTIVARIABLE AND LOSSLESS SYSTEMS
13 Review of Discrete-Time Multi-Input Multi-Output LTl Systems 660
13.0 Introduction 660
13.1 Multi-Input Multi-Output Systems 661
13.2 Matrix Polynomials 661
13.3 Matrix Fraction Descriptions 665
13.4 State Space Descriptions 669
13.5 The Smith-McMillan Form 687
13.6 Poles of Transfer Matrices 699
13.7 Zeros of Transfer Matrices 703
13.8 Degree of a Transfer Matrix 707
Contents ix
13.9 FIR Transfer Matrices 708
13.10 Causal Inverses of Causal Systems 711
Problems 715
14 Paraunltary and Lossless Systems 722
14.0 Introduction 722
14.1 A Brief History 723
14.2 Fundamentals of Lossless Systems 724
14.3 Lossless Systems with Two Outputs 727
14.4 Structures for Af x Af and M x 1 FIR Lossless Systems
14.5 State Space Manifestation of Lossless Property 740
14.6 Factorization of Unitary Matrices 745
14.7 Smith-McMillan Form and Pole-Zero Pattern 754
14.8 The Modulus Property 758
14.9 Structures for IIR Lossless Systems 759
14.10 Modified Lossless Structures 763
14.11 Preserving Lossless Property Under Quantization 768
14.12 Summary and Tables 771
Problems 775
APPENDICES
Introduction 782
Definitions and Examples 782
Basic Operations 783
Determinants 786
Linear Independence, Rank, and Related Issues 787
Eigenvalues and Eigenvectors 790
Special Types of Matrices 793
Unitary Triangularization 798
Maximization and Minimization 798
Properties Preserved in matrix products 799
Problems 800
A Review of Matrices 782
A.O
A.l
A.2
A.3
A.4
A.5
A.6
A.7
A.8
A.9
B Review of Random Processes
B.O
B.l
B.2
B.3
B.4
B.5
803
Introduction 803
Real Random Variables 803
Real Random Processes 806
Passage Through LTI Systems 810
The Complex Case 811
The Vector Case 812
C Quantization of Subband Signals 816
C.O Introduction 816
C.l Quantizer Noise Variance 816
C.2 The Ideal Subband Coder 818
C.3 The Orthogonal TYansform Coder 826
C.4 Similarities and Differences 833
x
Contents
C.5 Relation to Other Methods 839
Problems 845
D Spectral Factorization Techniques 849
D.O Introduction 849
D.l The Complex Cepstrum 849
D.2 A Cepstral Inversion Algorithm 853
D.3 A Spectral Factorization Algorithm 854
Problems 858
E Mason s Gain Formula 859
Glossary of Symbols 866
List of Important Summaries (Tables) 867
List of Important Summaries (Figures) 868
Bibliography 869
Alphabetical List of References Cited in the Book 869
Some References by Topic 888
Index 891
Contents XI
|
adam_txt |
Titel: Multirate systems and filter banks
Autor: Vaidyanathan, P. P
Jahr: 2006
Contents
Preface xi
PART 1 INTRODUCTORY CHAPTERS
1 Introduction 1
1.1 Major Developments 3
1.2 Scope andOutline 8
2 Review of Discrete-Time Systems 12
2.0 Introduction 12
2.1 Discrete-Time Signals 12
2.2 Multi-Input Multi-Output Systems 24
2.3 Notations 28
2.4 Discrete-Time Filters (Digital Filters) 31
Problems 39
3 Review of Digital Filters 42
3.0 Introduction 42
3.1 Filter Design Specifications 42
3.2 FIR Filter Design 45
3.3 IIR Filter Design 60
3.4 Ailpass Filters 71
3.5 Special Types of Filters 83
3.6 IIR Filters Based on Two Ailpass Filters 84
3.7 Concluding Remarks 91
Problems 93
4 Fundamentals of Multirate Systems 100
4.0 Introduction 100
4.1 Basic Multirate Operations 100
4.2 Interconnection of Building Blocks 118
4.3 The Polyphase Representation 120
4.4 Multistage Implementations 134
4.5 Some Applications of Multirate Systems 143
4.6 Special Filters and Filter Banks 151
4.7 Multigrid Methods 168
Problems 178
PART 2 MULTIRATE FILTER BANKS
5 Maximally Decimated Filter Banks 188
5.0 Introduction 188
5.1 Errors Created in the QMF Bank 191
5.2 A Simple Alias-Free QMF System 196
5.3 Power Symmetric QMF Banks 204
5.4 M-channel Filter Banks 223
5.5 Polyphase Representation 230
5.6 Perfect Reconstruction (PR) Systems 234
5.7 Alias-Free Filter Banks 245
5.8 Tree Structured Filter Banks 254
5.9 Transmultiplexers 259
5.10 Summary and Tables 266
Problems 272
6 Paraunitary Perfect Reconstruction (PR) Filter Banks 286
6.0 Introduction 286
6.1 Lossless Transfer Matrices 288
6.2 Filter Bank Properties Induced by Paraunitariness 294
6.3 Two Channel FIR Paraunitary QMF Banks 298
6.4 The Two Channel Paraunitary QMF Lattice 302
6.5 A/-channeI FIR Paraunitary Filter Banks 314
6.6 TVansform Coding and the "LOT" 322
6.7 Summary, Comparisons, and Tables 326
Problems 333
7 Linear Phase Perfect Reconstruction QMF Banks 337
7.0 Introduction 337
7.1 Some Necessary Conditions 337
7.2 Lattice Structures for Linear Phase FIR PR QMF Banks 339
7.3 Formal Synthesis of Linear Phase FIR PR QMF Lattice 347
Problems 351
8 Cosine Modulated Filter Banks 353
8.0 Introduction 353
8.1 The Pseudo QMF Bank 354
8.2 Design of the Pseudo QMF Bank 363
8.3 Efficient Polyphase Structures 370
8.4 Deeper Properties of Cosine Matrices 373
8.5 Cosine Modulated Perfect Reconstruction Systems 377
Problems 392
PART 3 SPECIAL TOPICS
9 Quantization Effects 394
9.0 Introduction 394
9.1 Types of Quantization Effects 394
9.2 Review of Standard Techniques 397
viii Contents
9.3 Noise Transmission in Multirate Systems 405
9.4 Noise in Filter Banks 408
9.5 Filter Bank Output Noise 412
9.6 Limit Cycles 416
9.7 Coefficient Quantization 418
Problems 424
10 Multirate Filter Bank Theory and Related Topics 427
10.0 Introduction 427
10.1 Block Filters, LPTV Systems and Multirate Filter Banks 427
10.2 Unconventional Sampling Theorems 436
Problems 454
11 The Wavelet Transform and its Relation to Multirate Filter Banks 457
11.0 Introduction 457
11.1 Background and Outline 458
11.2 The Short-Time Fourier Transform 463
11.3 The Wavelet Transform 481
11.4 Discrete-Time Orthonormal Wavelets 500
11.5 Continuous-Time Orthonormal Wavelet Basis 510
11.6 Concluding Remarks 536
Problems 539
12 Multidimensional Multirate Systems 545
12.0 Introduction 545
12.1 Multidimensional Signals 546
12.2 Sampling a Multidimensional Signal 555
12.3 Minimum Sampling Density 568
12.4 Multirate Fundamentals 572
.12.5 Alias-Free Decimation 597
12.6 Cascade Connections 603
12.7 Multirate Filter Design 608
12.8 Special Filters and Filter Banks 623
12.9 Maximally Decimated Filter Banks 627
12.10 Concluding Remarks 641
Problems 650
PART 4 MULTIVARIABLE AND LOSSLESS SYSTEMS
13 Review of Discrete-Time Multi-Input Multi-Output LTl Systems 660
13.0 Introduction 660
13.1 Multi-Input Multi-Output Systems 661
13.2 Matrix Polynomials 661
13.3 Matrix Fraction Descriptions 665
13.4 State Space Descriptions 669
13.5 The Smith-McMillan Form 687
13.6 Poles of Transfer Matrices 699
13.7 Zeros of Transfer Matrices 703
13.8 Degree of a Transfer Matrix 707
Contents ix
13.9 FIR Transfer Matrices 708
13.10 Causal Inverses of Causal Systems 711
Problems 715
14 Paraunltary and Lossless Systems 722
14.0 Introduction 722
14.1 A Brief History 723
14.2 Fundamentals of Lossless Systems 724
14.3 Lossless Systems with Two Outputs 727
14.4 Structures for Af x Af and M x 1 FIR Lossless Systems
14.5 State Space Manifestation of Lossless Property 740
14.6 Factorization of Unitary Matrices 745
14.7 Smith-McMillan Form and Pole-Zero Pattern 754
14.8 The Modulus Property 758
14.9 Structures for IIR Lossless Systems 759
14.10 Modified Lossless Structures 763
14.11 Preserving Lossless Property Under Quantization 768
14.12 Summary and Tables 771
Problems 775
APPENDICES
Introduction 782
Definitions and Examples 782
Basic Operations 783
Determinants 786
Linear Independence, Rank, and Related Issues 787
Eigenvalues and Eigenvectors 790
Special Types of Matrices 793
Unitary Triangularization 798
Maximization and Minimization 798
Properties Preserved in matrix products 799
Problems 800
A Review of Matrices 782
A.O
A.l
A.2
A.3
A.4
A.5
A.6
A.7
A.8
A.9
B Review of Random Processes
B.O
B.l
B.2
B.3
B.4
B.5
803
Introduction 803
Real Random Variables 803
Real Random Processes 806
Passage Through LTI Systems 810
The Complex Case 811
The Vector Case 812
C Quantization of Subband Signals 816
C.O Introduction 816
C.l Quantizer Noise Variance 816
C.2 The Ideal Subband Coder 818
C.3 The Orthogonal TYansform Coder 826
C.4 Similarities and Differences 833
x
Contents
C.5 Relation to Other Methods 839
Problems 845
D Spectral Factorization Techniques 849
D.O Introduction 849
D.l The Complex Cepstrum 849
D.2 A Cepstral Inversion Algorithm 853
D.3 A Spectral Factorization Algorithm 854
Problems 858
E Mason's Gain Formula 859
Glossary of Symbols 866
List of Important Summaries (Tables) 867
List of Important Summaries (Figures) 868
Bibliography 869
Alphabetical List of References Cited in the Book 869
Some References by Topic 888
Index 891
Contents XI |
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id | DE-604.BV022882109 |
illustrated | Illustrated |
index_date | 2024-07-02T18:50:50Z |
indexdate | 2024-07-09T21:07:39Z |
institution | BVB |
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record_format | marc |
series2 | Prentice Hall signal processing series |
spelling | Vaidyanathan, P. P. Verfasser aut Multirate systems and filter banks P. P. Vaidyanathan 1. impr. Delhi Dorling Kindersley 2006 XVI, 911 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Prentice Hall signal processing series Literaturverz. S. 869 - 887 Filterbank (DE-588)4154389-0 gnd rswk-swf Digitale Signalverarbeitung (DE-588)4113314-6 gnd rswk-swf Digitalfilter (DE-588)4070477-4 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Digitalfilter (DE-588)4070477-4 s DE-604 Digitale Signalverarbeitung (DE-588)4113314-6 s Filterbank (DE-588)4154389-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016087070&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Vaidyanathan, P. P. Multirate systems and filter banks Filterbank (DE-588)4154389-0 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd Digitalfilter (DE-588)4070477-4 gnd |
subject_GND | (DE-588)4154389-0 (DE-588)4113314-6 (DE-588)4070477-4 (DE-588)4143389-0 |
title | Multirate systems and filter banks |
title_auth | Multirate systems and filter banks |
title_exact_search | Multirate systems and filter banks |
title_exact_search_txtP | Multirate systems and filter banks |
title_full | Multirate systems and filter banks P. P. Vaidyanathan |
title_fullStr | Multirate systems and filter banks P. P. Vaidyanathan |
title_full_unstemmed | Multirate systems and filter banks P. P. Vaidyanathan |
title_short | Multirate systems and filter banks |
title_sort | multirate systems and filter banks |
topic | Filterbank (DE-588)4154389-0 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd Digitalfilter (DE-588)4070477-4 gnd |
topic_facet | Filterbank Digitale Signalverarbeitung Digitalfilter Aufgabensammlung |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016087070&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT vaidyanathanpp multiratesystemsandfilterbanks |