Digital Audio Signal Processing (eBook)

Udo Z lzer (Autor)

eBook Download: EPUB

2022 | 3. Auflage
416 Seiten
Wiley (Verlag)
978-1-119-83269-0 (ISBN)

Infos

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.

Udo Zölzer is Professor of Signal Processing and Communication at Helmut Schmidt University, Hamburg, Germany. His research interests include audio and video signal processing and communications. He is the author of several books including DAFX: Digital Audio Effects.

Textauszug

Chapter 1
Introduction

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 can be written as a convolution operation given by

(1.31)

which is shown in the bottom left plot of Fig. 1.6. The Fourier transforms of the individual signals for sampling are given by

(1.32)

(1.33)

(1.34)

(1.35)

and are shown in Fig. 1.6 (right column). Sampling leads to the periodic extension of the baseband spectrum at multiples of the sampling rate and the scaling by . The reconstruction of

(1.36)

(1.37)

is achieved by convolution with a system impulse...

Produkt-Details

• Erscheint lt. Verlag: 24.2.2022
• Sprache: englisch
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Audio & Speech Processing & Broadcasting • Audio-, Sprachverarbeitung u. Übertragung • Computer Engineering • Computertechnik • Digitale Signalverarbeitung • Electrical & Electronics Engineering • Elektrotechnik u. Elektronik • Signal Processing • Signalverarbeitung
• ISBN-10: 1-119-83269-1 / 1119832691
• ISBN-13: 978-1-119-83269-0 / 9781119832690