Signals and Systems for Speech and Hearing

by Stuart Rosen & Peter Howell

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"These authors have determined to walk the fine line between simplicity and truth ... [and]  have succeeded in their goal of clarifying what can be an esoteric subject, in my opinion quite admirably" J.F. Bartram, Journal of the Acoustical Society of America (Vol 94:5 p 3530).

An introductory textbook from Emerald Group Publishing (1991).

ISBN 0-12-597231-8 pbk

A new edition of this book was available from the end of 2010 (details here).

In essence, this book addresses the problem of presenting highly technical material to those who lack advanced technical training. This is done with minimal mathematics but over 300 figures (all drawn specifically for the book), and integrated closely with the text (no figure numbers are used). Exercises are provided at the end of most chapters. For details of the way in which the book has been used in an introductory course primarily for audiologists, click here.

EXCERPTS FROM THE PREFACE.

Many people working in the speech and hearing sciences come from non-technical backgrounds, making it difficult for them to master the essential technical underpinnings of the area. Perhaps the main barrier to acquiring knowledge in this area is that available textbooks nearly always assume an audience consisting of students of engineering. It is relatively difficult for the non-engineer, even with sufficient mathematical expertise, to get much out of these books. For readers without a knowledge of calculus, it is well nigh impossible.

The problem of patchy understanding of basic technical concepts is acknowledged, at least implicitly, in most books dealing with speech and hearing. Nearly all begin with an introductory chapter purporting to cover the topics explored in this book - from relatively straightforward ones like the nature of sine waves and the calculation of decibels to the much more complex ideas of Fourier analysis and synthesis. Only those who already know this material are likely to appreciate its significance, and they do not need to read such a chapter. It seemed to us that only an entire book could cover in a sensible and thorough way the main concepts required. Furthermore, although we realized that there are some students who could handle a highly mathematical text, there are many who would have no mathematical training beyond algebra and trigonometry. Therefore, we decided to try to tell the entire story in words and pictures, with only minimal mathematics.

We have attempted to provide the reader with a thorough introduction to the concepts of signals and systems analysis that play a role in the speech and hearing sciences. Few equations are used, and we have tried to maintain an informal, friendly and informative style throughout. Readers who like their technical material straight will, we hope, forgive us our little jokes. Because much of the story is told through figures, we have gone to great lengths to provide clear and truthful figures that show what the text says they do! We hope the reader will come away with a strong visual understanding of the concepts involved.

This book can be used at many levels, from the student who hasn't heard of a spectrum before, to the experienced worker who has only a fuzzy understanding of the notion of an impulse response. We have tried to keep the underlying conceptual structure of signals and systems analysis explicit, in the hope that even some readers with advanced technical training might find clarification of the basic principles.

ANNOTATED TABLE OF CONTENTS.

Chapter 1 - Introduction - The relevance of studying the properties of signals and systems for work in the speech and hearing sciences; examples of signals and systems; input and output signals.

Chapter 2 - Signals in the real world - the similarity of acoustic, mechanical and electrical signals; transduction.

Chapter 3 - Introduction to signals - The specification and construction of sinusoids; the concepts of frequency, period, amplitude and phase; periodic and aperiodic sounds; measures of amplitude - peak- to-peak, rms; dB scales.

Chapter 4 - Introduction to systems - Linearity, additivity, homogeneity and time-invariance. Saturating nonlinearities. Application to middle ear and basilar membrane vibration, and to tape recorders.

Chapter 5 - A preview - If we know what a linear time-invariant system does to sinusoids, we know what it will do to any signal.

Chapter 6 - The frequency response of systems - Amplitude responses as the ratio of output levels to input levels at particular frequencies. Low-pass, high-pass, band-pass and band-stop filters. The use of logarithmic axes (dB vs log Hz). The amplitude response of a cascade of systems. Application to middle ear vibrations and vocal tracts of varying shapes. Formants as resonances. Phase responses, linear and otherwise.

Chapter 7 - The frequency characterization of signals - Fourier analysis and synthesis. The amplitude and phase spectra of periodic signals: sinusoids, sawtooths, square waves, triangle waves and pulse trains. The spectra of aperiodic signals: transients and noise.

Chapter 8 - Signals through systems - Determining the output of systems to specified signals in the frequency domain, for both amplitude and phase. A sawtooth through ideal and realistic low-pass filters. Noise through a filter. Distortion.

Chapter 9 - The time characterization of systems - The notion of an impulse, and the impulse response. The relationship between the frequency response of a system and its impulse response. Determining the frequency response of a set of headphones in 3 ways: via the impulse response, a sinusoid swept in frequency, and white noise.

Chapter 10 - The relationship between the time and frequency domains - Signals short in time tend to be wide in spectrum, and vice versa. The trade-off between temporal resolution and frequency resolution in band-pass filters. The relationship between a system's impulse response and its frequency response.

Chapter 11 - Spectrograms: Practical short-term spectral analysis - Determining dynamic spectral changes; the notion of a filter bank; rectification and smoothing; short-term spectra; the use of wide- and narrow-band filters; making spectrograms in the time domain; windowing.

Chapter 12 - Applications to hearing - The measurement of frequency responses, and notions of linearity and nonlinearity in the peripheral auditory system: head and pinna, the ear canal resonance, middle ear vibration, basilar membrane motion; modelling the auditory system as a set of systems; measuring the auditory filter behaviorally.

Chapter 13 - Applications to speech production - The source-filter theory of speech production and its application to vowels, diphthongs and fricatives.

Chapter 14 - Digital signals and systems - sampling and quantization; digital-to-analog and analog-to-digital conversion; aliasing; simple digital systems.

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