Digital Audio Signal Processing E-Book

Udo Zölzer

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 463

Veröffentlichungsjahr: 2022

Beschreibung

Digital Audio Signal Processing

The fully revised new edition of the popular textbook, featuring additional MATLAB exercises and new algorithms for processing digital audio signals

Digital Audio Signal Processing (DASP) techniques are used in a variety of applications, ranging from audio streaming and computer-generated music to real-time signal processing and virtual sound processing.

Digital Audio Signal Processing provides clear and accessible coverage of the fundamental principles and practical applications of digital audio processing and coding. Throughout the book, the authors explain a wide range of basic audio processing techniques and highlight new directions for automatic tuning of different algorithms and discuss state- of-the-art DASP approaches. Now in its third edition, this popular guide is fully updated with the latest signal processing algorithms for audio processing. Entirely new chapters cover nonlinear processing, Machine Learning (ML) for audio applications, distortion, soft/hard clipping, overdrive, equalizers and delay effects, sampling and reconstruction, and more.

• Covers the fundamentals of quantization, filters, dynamic range control, room simulation, sampling rate conversion, and audio coding
• Describes DASP techniques, their theoretical foundations, and their practical applications
• Discusses modern studio technology, digital transmission systems, storage media, and home entertainment audio components
• Features a new introductory chapter and extensively revised content throughout
• Provides updated application examples and computer-based activities supported with MATLAB exercises and interactive JavaScript applets via an author-hosted companion website

Balancing essential concepts and technological topics, Digital Audio Signal Processing, Third Edition remains the ideal textbook for advanced music technology and engineering students in audio signal processing courses. It is also an invaluable reference for audio engineers, hardware and software developers, and researchers in both academia and industry.

Leseprobe

Digital Audio Signal Processing

Third Edition

Udo Zölzer

Helmut Schmidt University Hamburg, Germany

with

Martin Holters, Etienne Gerat, Patrick Nowak, Purbaditya Bhattacharya, Lasse Köper, and Daniel Ahlers

This third edition first published 2022

© 2022 John Wiley & Sons Ltd

Edition History: 1e (1997); 2e (2008)

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The right of Udo Zölzer to be identified as the author of this work has been asserted in accordance with law.

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Library of Congress Cataloging‐in‐Publication data

Name: Zölzer, Udo, author.

Title: Digital audio signal processing / Udo Zölzer, Helmut Schmidt

 University Hamburg, Germany with Martin Holters, Etienne Gerat, Patrick

 Nowak, Purbaditya Bhattacharya, Lasse Köper, and Daniel Ahlers.

Other titles: Digitale Audiosignalverarbeitung. English

Description: Third edition. | Hoboken : Wiley, 2022. | Includes

 bibliographical references and index.

Identifiers: LCCN 2021059110 (print) | LCCN 2021059111 (ebook) | ISBN

 9781119832676 (cloth) | ISBN 9781119832683 (adobe pdf) | ISBN

 9781119832690 (epub)

Subjects: LCSH: Sound–Recording and reproducing–Digital techniques. |

 Signal processing–Digital techniques.

Classification: LCC TK7881.4 .Z6513 2022 (print) | LCC TK7881.4 (ebook) |

 DDC 621.389/3–dc23/eng/20220103

LC record available at https://lccn.loc.gov/2021059110

LC ebook record available at https://lccn.loc.gov/2021059111

Cover Design: Wiley

Cover Image: © whiteMocca/Shutterstock

Preface for the Third Edition

This 3rd Edition is a revised and extended version of the book. It offers three new chapters (1, 10, and 11) and extensions on a further four chapters (5, 7, 8, and 9). The content of this book is the basis of a course on Digital Audio Signal Processing at the Hamburg University of Technology (TUHH) and a course on Multimedia Signal Processing at the Helmut Schmidt University Hamburg. For further study, you can find lecture slides, exercises, Matlab examples, and interactive audio demonstrations on the website.

https://mydasp.com/dasp.

My thanks go to Dr. Martin Holters for the interactive audio demonstrations and maintaining the website http://www.dafx.de . Thanks also to him and Lasse Köper for their contribution to the new Chapter 10 on “Nonlinear Processing”. I would like to thank Daniel Ahlers for his contributions and updates to Chapter 5 on “Audio Processing Systems”. Purbaditya Bhattacharya and Patrick Nowak made contributions to Chapter 7 on “Room Simulation” and are mainly responsible for the new Chapter 11 on “Machine Learning for Audio”. Purbaditya Bhattacharya also made contributions to Chapter 9 on “Audio Coding”. Thanks to both of them. Finally, I would like to thank Etienne Gerat for his refinements and extensions to Chapter 8 on “Dynamic Range Control”. Last but not least, I would like to thank all participants of the lectures over all these years who have been my driving force:‐).

Udo Zölzer

Hamburg, January 2022

Preface for the Second Edition

This 2nd Edition represents a revised and extended version, and offers an improved description as well as new issues and extended references. The content of this book is the basis of a course on Digital Audio Signal Processing at the Hamburg University of Technology (TU Hamburg‐Harburg) and a course on Multimedia Signal Processing at the Helmut Schmidt University Hamburg. For further study, you can find interactive audio demonstrations, exercises, and Matlab examples on the website.

http://ant.hsu‐hh.de/dasp/.

In addition to the basics of digital audio signal processing introduced in this 2nd edition, further advanced algorithms for digital audio effects can be found in the book DAFX – Digital Audio Effects (Ed. U. Zölzer) with a related website.

http://www.dafx.de.

My thanks go to Prof. Dieter Leckschat, Dr. Gerald Schuller, Udo Ahlvers, Mijail Guillemard, Christian Helmrich, Martin Holters, Dr. Florian Keiler, Stephan Möller, Francois‐Xavier Nsabimana, Christian Ruwwe, Harald Schorr, Dr. Oomke Weikert, Catja Wilkens, and Christian Zimmermann.

Udo Zölzer

Hamburg, December 2007

Preface for the First Edition

Digital audio signal processing is employed in recording and storing music and speech signals, for sound mixing and production of digital programs, in digital transmission to broadcast receivers as well as in consumer products like CDs, DATs, and PCs. In the latter case, the audio signal is in a digital form all the way from the microphone up to the loudspeakers, enabling real‐time processing with fast digital signal processors.

This book provides the basis of an advanced course in Digital Audio Signal Processing which I have been giving since 1992 at the Technical University Hamburg‐Harburg. It is directed at students studying engineering, computer science, and physics but is also for professionals who are looking for solutions to problems in audio signal processing in the fields of studio engineering, consumer electronics, and multimedia. The mathematical and theoretical fundamentals of digital audio signal processing systems will be presented and typical applications with an emphasis on realization aspects will be discussed. Prior knowledge of systems theory, digital signal processing, and multirate signal processing are assumed as a prerequisite.

The book is divided into two parts. The first part (Chapters 1–4) presents a basis for hardware systems used in digital audio signal processing. The second part (Chapters 5–9) discusses algorithms for processing digital audio signals. Chapter 1 describes the course taken by an audio signal from its recording in a studio up to its reproduction at home. Chapter 2 contains a representation of signal quantization, dither techniques, and spectral shaping of quantization errors used for reducing the nonlinear effects of quantization. In the end, a comparison is made between the fixed‐point and floating‐point number representations as well as their associated effects on format conversion and algorithms. Chapter 3 describes methods for AD/DA conversion of signals, starting with Nyquist sampling, methods for oversampling techniques, and delta‐sigma modulation. The chapter closes with a presentation of some circuit design of AD/DA converters. After an introduction to digital signal processors and digital audio interfaces, Chapter 4 describes simple hardware systems based on single‐ and multiprocessor solutions. The algorithms introduced in Chapters 5–9 are, to a great extent, implemented in real‐time on the hardware platforms presented in Chapter 4. Chapter 5 describes digital audio equalizers. Apart from the implementation aspects of recursive audio filters, non‐recursive linear phase filters based on fast convolution and filter banks are introduced. Filter designs, parametric filter structures, and precautions for reducing quantization errors in recursive filters are dealt with in detail. Chapter 6 deals with room simulation. Methods for simulation of artificial room impulse response and methods for approximation of measured impulse responses are discussed. In Chapter 7, the dynamic range control of audio signals is described. These methods are applied at several positions in the audio chain from the microphone to the loudspeakers to adapt to the dynamics of the recording, transmission, and listening environment. Chapter 8 contains a presentation of methods for synchronous and asynchronous sampling rate conversion. Efficient algorithms are described which are suitable for real‐time processing as well as off‐line processing. Both lossless and lossy audio coding are discussed in Chapter 9. Lossless audio coding is applied for the storage of higher word lengths. Lossy audio coding, however, plays a significant role in communication systems.

I would like to thank Prof. Fliege (University of Mannheim), Prof. Kammeyer (University of Bremen), and Prof. Heute (University of Kiel) for comments and support. I am also grateful to my colleagues at the TUHH and especially Dr. Alfred Mertins, Dr. Thomas Boltze, Dr. Bernd Redmer, Dr. Martin Schönle, Dr. Manfred Schusdziarra, Dr. Tanja Karp, Georg Dickmann, Werner Eckel, Thomas Scholz, Rüdiger Wolf, Jens Wohlers, Horst Zölzer, Bärbel Erdmann, Ursula Seifert, and Dieter Gödecke. Additionally, I would like to say a word of gratitude to all those students who helped me in carrying out this work successfully.

Special thanks go to Saeed Khawaja for his help during translation and to Dr. Anthony Macgrath for proof‐reading the text. I also would like to thank Jenny Smith, Colin McKerracher, Ian Stoneham, and Christian Rauscher (Wiley).

My special thanks are directed to my wife Elke and my daughter Franziska.

Udo Zölzer

Hamburg, July 1997

Chapter 1Introduction

U. Zölzer

In this first chapter, we will introduce the basics of signals and systems, and describe the transmission of signals through these systems [Opp14]. These fundamental concepts and the describing algorithms lay the foundation for digital audio signal processing. We will start with analog signals and analog systems, then we will sample the analog signals and perform digital signal processing, and finally reconstruct an analog output signal from the digital output signal. Figure 1.1 shows a typical audio application of capturing a vocalist and transmission to a loudspeaker via an amplifier for reproduction in another room for a listener or listening audience. The microphone delivers an electrical input signal and the output signal is the signal that will be received by the listener's ear. Both signals are continuous‐time input and output signals. The entire chain of operations from microphone, amplifier, loudspeaker, and sound transmission through the listening room to the listener can be modeled by a system with a continuous‐time impulse response . Such an impulse response can be acquired by an impulse response measurement approach. The entire continuous‐time approach description can also be represented by a discrete‐time approach through sampling the microphone signal , using the discrete‐time impulse response , and then delivering the output signal . Both continuous‐time and discrete‐time signal‐processing techniques [Opp10, Opp14] will be introduced in the following sections.

1.1 Continuous‐time Signals and Convolution

Continuous‐time signals, as shown in Fig. 1.2, can be used as test signals to analyze the behavior of the response of a physical system to an excitation signal. We need a few simple test signals that will allow for the derivation of all important relations to obtain the input/output description of an input signal transformed to an output signal (handclap acoustical transmission through room received by human ear). The rectangular (rect) function is defined by

Figure 1.1 Audio capturing and reproduction for a listener, and representations of the operations by a signal and system model with input and output signals and by a system represented by an impulse response.

Figure 1.2 Continuous‐time signals , , , , , and .

(1.1)

The Dirac impulse is defined by

(1.2)

The step function is defined by

(1.3)

A general signal can be written using the sampling property of the Dirac impulse as

(1.4)

Continuous‐time systems transform the input to the output . A time‐domain description can be given by the following signal flow graph: . The system parameter inside the box is called the impulse response of the system. It describes the output of the system when the input is the Dirac . Using Eq. (1.4), we can easily derive that the input/output relation of a system with impulse response is given by the integral (sliding the folded impulse response along the input and performing weighting and integration)

(1.5)

which is called continuous‐time convolution. The convolution integral describes a filter operation and is written as . Causality of a system implies for and stability of a system is achieved if the integral of impulse response . A simple example for continuous‐time convolution is demonstrated in Fig. 1.3.

Figure 1.3 Continuous‐time convolution showing the folded version of the impulse response and shifted versions for .

Using the complex exponential as input with , the output is given by the convolution integral as

(1.6)

(1.7)

This shows that for a exponential input , the output is again an exponential signal where the input signal is weighted by the complex number , which is the Fourier transform (integral) of the impulse response , and is also called the frequency response of a continuous‐time system given by

(1.8)

From , we can compute the magnitude response

(1.9)

and the phase response

(1.10)

of a continuous‐time system. For a given signal , we can give its continuous‐time Fourier transform as

(1.11)

The Fourier integral describes a spectral transform from time domain to frequency domain , which is called the Fourier spectrum or Fourier transform of . The inverse continuous‐time Fourier transform is given by

(1.12)

which takes the Fourier spectrum and reconstructs the input . In the following, useful Fourier transform pairs are listed in Eqs. (1.13)–(1.23). An important relation between the time domain , using and giving , and frequency domain , using and giving , shows that convolution in the time domain can be described by multiplication in the frequency domain.

Fourier Transform Pairs1

(1.13)

(1.14)

(1.15)

(1.16)

(1.17)

(1.18)

(1.19)

(1.20)

(1.21)

(1.22)

(1.23)

Fourier Transforms of Even and Causal Signals

Figure  1.4 shows the Fourier transforms of even and causal rect signals and Fig. 1.5 shows two even sinc signals and their Fourier transforms. The ripple in the passband is based on the truncated length of the sinc signal.

Figure 1.4 Fourier transforms of an even and a causal rect signal. The small imaginary part of the lower left plot arises from a small asymmetry of the rect signal in the upper left plot.

Figure 1.5 Fourier transforms of two even sinc signals.

1.2 Continuous‐time Fourier Transform and Laplace Transform

The extension of the continuous‐time Fourier transform to the Laplace transform allows for the transform of signals and impulse responses where the Fourier transform does not converge but the Laplace transform converges for a given convergence region. This extension of the continuous‐time Fourier transform

(1.24)

is achieved by introducing a real part to the imaginary part according to a new complex variable , which then gives

(1.25)

(1.26)

and thus the Laplace transform

(1.27)

The Laplace transform of signals often leads to a rational function with a numerator polynomial and a denominator polynomial in the variable . The zeros of the numerator are called the zeros of and the zeros of are called the poles of . The rational function can be in given in polynomial, pole/zero, and partial expansion forms.

1.3 Sampling and Reconstruction

For digital signal processing, the sampling of with a sampling rate and a sampling interval is performed, which leads to a sequence of numbers with time index . According to the sampling theorem, the input signal must be band limited to . The sampling and the reconstruction of from the number sequence is achieved by the following sequence of operations: . Both operations are performed by an analog‐to‐digital converter (ADC) and a digital‐to‐analog converter (DAC). The converters can be considered as mixed continuous‐time and discrete‐time systems.

Sampling and quantization (analog‐to‐digital conversion) can be described by

(1.28)

(1.29)

(1.30)

where the input is sampled by multiplying it with a series of Dirac impulses giving the ideal sampled and then quantization of the samples to the sequence of numbers with a finite number representation. Figure 1.6 shows in the left column the time‐domain signals involved.

Figure 1.6 Sampling and reconstruction – Time‐domain signals (left column) and corresponding Fourier spectra (right column).

Reconstruction (digital‐to‐analog conversion) of the continuous‐time from the sampled sequence