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2-2 Section Two

called time-frequency analysis. Its justification is that tones or pitch (which are frequency like)
can exist and be perceived over a short time interval, after which they may change as indicated by
notes in a musical score, for example. The spectrogram used in speech research is an early exam-
ple of this approach. The objective of time-frequency analysis is to locate the signal energy in
various frequency ranges during different time intervals.

Computers software is available to perform rapid transformations between time and fre-

quency domains or to generate joint-domain representations of signals. Many computationally
difficult or burdensome operations are carried out quickly and accurately. With the aid of a com-
puter, virtually all the interesting audio spectrum and signal characteristics can be captured, dis-
played, and analyzed.

In computer-aided analysis of audio signals, discrete-time signals are used. These are formed

by sampling the actual continuum of signal values at equally spaced instants in time. In principle,
no information is lost through the sampling process if it is performed properly. Advanced digital
signal analysis techniques play an important role both in objective technical assessment of audio
equipment and in human auditory perception of sound quality.

In summary, analysis of signal and spectrum characteristics or, simply, spectral analysis is a

quantitative means to assess audio signals and audio signal-processing systems as well as general
audio quality. Additionally, certain features contained in or derived from the spectrum do corre-
late well with human perception of sound. Although the basis of spectral analysis is mathemati-
cal, considerable insight and understanding can be gained from a study of the several examples
of time-domain and frequency-domain interrelationships provided in this section.

In This Section:

Chapter 2.1: Signals and Spectra

2-7

Introduction

2-7

Signal Energy and Power

2-7

Sinusoids and Phasor Representation

2-8

Line Spectrum

2-10

Fourier-Series Analysis

2-12

Discrete Fourier Series

2-14

Spectral Density and Fourier Transformation

2-16

Impulse Signal

2-18

Power Spectrum

2-19

Analytic Signal

2-20

Bibliography

2-22

Chapter 2.2: Spectral Changes and Linear Distortion

2-25

Introduction

2-25

Distortion Mechanisms

2-25

Linear Range

2-26

Spectra Comparison

2-26

Sinusoidal Steady-State Measurements

2-27

Some Effects of Frequency Response on Transient Signals

2-32

Phase Delay and Group Delay

2-37

Distortionless Processing of Signals

2-39

Linear Phase and Minimum Phase

2-42

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The Audio Spectrum

The Audio Spectrum 2-3

Bandwidth and Rise Time

2-45

Echo Distortion

2-46

Classifications of Phase Distortion

2-48

Bibliography

2-50

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The Audio Spectrum

2-4 Section Two

Lynn, P. A.: An Introduction to the Analysis and Processing of Signals, 2nd ed. Macmillan, Lon-

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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)

Copyright © 2004 The McGraw-Hill Companies. All rights reserved.

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The Audio Spectrum

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Any use is subject to the Terms of Use as given at the website.

The Audio Spectrum