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Introduction to Audio Signal Processing

Introduction  to Audio Signal Processing
Introduction  to Audio Signal Processing

Audio signal processing is at the heart of recording, enhancing, storing and transmitting audio content. Audio signal processing is used to convert between analog and digital formats, to cut or boost selected frequency ranges, to remove unwanted noise, to add effects and to obtain many other desired results. Today, this process can be done on an ordinary PC or laptop, as well as specialized recording equipment.


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Overview

Audio signal processing is at the heart of recording, enhancing, storing and transmitting audio content. Audio signal processing is used to convert between analog and digital formats, to cut or boost selected frequency ranges, to remove unwanted noise, to add effects and to obtain many other desired results. Today, this process can be done on an ordinary PC or laptop, as well as specialized recording equipment.

Warren Koontz provides an introduction to this important topic with an emphasis on digital audio signal processing. Starting with a basic overview of sound and analog audio signals, he proceeds through the processes of sampling and quantizing to digital audio signals. The book introduces and develops both time and frequency domain processing of digital audio signals and, in the later chapters, examines specific applications such as equalizer design, effect generation and file compression.

Introduction to Audio Signal Processing will appeal to undergraduate engineering and engineering technology students. Using examples and exercises with MATLAB scripts and functions, including MATLAB streaming audio, students will be able to process audio in real time on their own PC.

About the Author
Warren Koontz is Professor Emeritus in the College of Applied Science and Technology at Rochester Institute of Technology. He received a B.S. degree from the University of Maryland, a M.S. degree from the Massachusetts Institute of Technology and a Ph.D. degree from Purdue University, all in electrical engineering. Koontz spent more than thirty years at Bell Laboratories developing and managing the development of digital transmission systems. After retiring from Bell Labs, he joined the faculty of the Electrical, Computer and Telecommunication Engineering Technology department at RIT where he helped create an Audio Engineering Technology option that is offered in the ECTET department. Koontz has continued his research in the field of audio engineering and he has published and presented results of his research.

Details

Publisher: RIT Press (12/2016)
ISBN-13: 978-1-939125-41-5
Binding: Softcover
Pages: 184
Illustrations: 128
Size: 7 x 10 in.
Shipping Weight: 1lb

Table of Contents

List of Figures x

List of Tables xiii

Nomenclature xiv

1 Introduction 1

2 Analog Audio Signals 4

2.1 Acoustic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Basic Analog Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Sinusoidal Signals . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.2 Periodic Signals . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.3 Random Signals . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Analog Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.1 Impulse Response Model of an LTIS . . . . . . . . . . . . . . 14

2.3.2 Dierential Equation Model of an LTIS . . . . . . . . . . . . 20

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Digital Coding of Sound 28

3.1 Digital Representation of an Analog Signal . . . . . . . . . . . . . . 28

3.2 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.1 Aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2.2 Down- and Upsampling . . . . . . . . . . . . . . . . . . . . . 33

3.2.3 Resampling Methods . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Quantizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3.1 Quantization Error . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.2 Nonlinear Quantization . . . . . . . . . . . . . . . . . . . . . 41

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4 Digital Audio Signal Processing 45

4.1 Basic Digital Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.1 Digital Impulse Function . . . . . . . . . . . . . . . . . . . . 45

4.1.2 Digital Unit Step Function . . . . . . . . . . . . . . . . . . . 46

4.1.3 Digital Everlasting Exponential Signal . . . . . . . . . . . . . 46

4.1.4 Periodic Digital Functions . . . . . . . . . . . . . . . . . . . . 47

4.2 Digital LTIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.1 Digital LTIS Impulse Response . . . . . . . . . . . . . . . . . 47

4.2.2 LTIS Frequency Response . . . . . . . . . . . . . . . . . . . . 49

4.2.3 The z-Transform . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2.4 Dierence Equation Model . . . . . . . . . . . . . . . . . . . 53

4.2.5 Poles and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.3 Fourier Analysis of Digital Signals and Systems . . . . . . . . . . . . 58

4.3.1 Discrete-Time Fourier Series . . . . . . . . . . . . . . . . . . 58

4.3.2 Discrete-Time Fourier Transform . . . . . . . . . . . . . . . . 62

4.3.3 DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.3.4 Interim Summary . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.3.5 Circular Convolution . . . . . . . . . . . . . . . . . . . . . . . 64

4.3.6 Fast Convolution of Long Signals . . . . . . . . . . . . . . . . 66

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5 Spectral Analysis of Audio Signals 70

5.1 Spectra of Signal Segments . . . . . . . . . . . . . . . . . . . . . . . 70

5.2 Spectral Analysis of Changing Sounds . . . . . . . . . . . . . . . . . 73

5.3 Real-Time Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . 79

5.4 Spectrum of Resampled Signals . . . . . . . . . . . . . . . . . . . . . 81

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6 Frequency-Shaping Filters 84

6.1 A Simple Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.2 Second-Order Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.2.1 Second-Order Peak Filter . . . . . . . . . . . . . . . . . . . . 87

6.2.2 Shelf Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.2.3 MATLAB Implementation . . . . . . . . . . . . . . . . . . . . 90

6.2.4 Audio Equalizer . . . . . . . . . . . . . . . . . . . . . . . . . 91

6.3 Low-Pass Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6.3.1 Low-Pass Filter Specication . . . . . . . . . . . . . . . . . . 92

6.3.2 Butterworth Low-Pass Filter . . . . . . . . . . . . . . . . . . 92

6.3.3 Other Low-Pass Filters . . . . . . . . . . . . . . . . . . . . . 96

6.4 High-Pass, Band-Pass, and Band-Stop Filters . . . . . . . . . . . . . 96

6.5 State-Space Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.5.1 State-Space Model of a Recursive Filter . . . . . . . . . . . . 99

6.5.2 A Useful State-Space Filter . . . . . . . . . . . . . . . . . . . 100

6.6 Filters and Source Models . . . . . . . . . . . . . . . . . . . . . . . . 102

6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7 Audio Eect Generation 106

7.1 Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.1.1 Fading In and Out . . . . . . . . . . . . . . . . . . . . . . . . 107

7.1.2 Cross-Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

7.2 Flanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7.3 Chorus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

7.4 Wah-Wah . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.5 Dynamic Range Control . . . . . . . . . . . . . . . . . . . . . . . . . 116

7.6 Tempo Change and Pitch Shifting . . . . . . . . . . . . . . . . . . . 120

7.6.1 Time Domain Methods . . . . . . . . . . . . . . . . . . . . . 120

7.6.2 Frequency Domain Methods . . . . . . . . . . . . . . . . . . . 121

7.6.3 Limitations of the Basic Tempo and Pitch Change Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.7 Noise Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

7.7.1 Noise Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.7.2 Noise Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . 126

7.7.3 MATLAB Implementation . . . . . . . . . . . . . . . . . . . . 127

7.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

8 Reverberation 130

8.1 Swept-Sine Measurement of Impulse Response . . . . . . . . . . . . . 131

8.2 Reverb Eect Building Blocks . . . . . . . . . . . . . . . . . . . . . . 134

8.2.1 Delay Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

8.2.2 Comb Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

8.2.3 All-Pass Filters . . . . . . . . . . . . . . . . . . . . . . . . . . 138

8.2.4 Scattering Matrix . . . . . . . . . . . . . . . . . . . . . . . . 139

8.3 Schroeder Reverberators . . . . . . . . . . . . . . . . . . . . . . . . . 139

8.4 State-Space Reverberators . . . . . . . . . . . . . . . . . . . . . . . . 141

8.5 Reverberators Using Multiport Elements . . . . . . . . . . . . . . . . 143

8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

9 Audio Compression 147

9.1 Polyphase Analysis and Synthesis Filters . . . . . . . . . . . . . . . . 148

9.1.1 Analysis Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 148

9.1.2 Interpolation Filter . . . . . . . . . . . . . . . . . . . . . . . . 152

9.1.3 MPEG Layer 1 Implementation . . . . . . . . . . . . . . . . . 154

9.2 Psychoacoustic Model . . . . . . . . . . . . . . . . . . . . . . . . . . 156

9.2.1 Sound Pressure Level Analysis . . . . . . . . . . . . . . . . . 156

9.2.2 Threshold of Hearing . . . . . . . . . . . . . . . . . . . . . . . 157

9.2.3 Frequency Masking . . . . . . . . . . . . . . . . . . . . . . . . 158

9.2.4 Global Masking Threshold and Signal-to-Mask Ratio . . . . . 162

9.3 Subband Sample Coding . . . . . . . . . . . . . . . . . . . . . . . . . 163

9.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Bibliography 164

Index 167

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