SIGNALS, SOUND, AND SENSATION

William M. Hartmann

*Signals, Sound, and Sensation* is a text about
signals, audio, acoustics, and mainly psychoacoustics.
It assumes that the reader is comfortable with elementary
calculus.
It can be purchased from:

**Springer-Verlag
333 Meadowlands Parkway
Secaucus, NJ, 07094
TOLL FREE: 1-800-777-4643**

CONTENTS

Chapter 1. The Pure Tone

Mathematics of the pure tone

* H.R. Hertz

The spectrum

The importance of the pure tone in psychoacoustics

The sound of a pure tone

Chapter 2. Complex Representation

Complex numbers - rectangular form

Complex numbers - polar form

Addition of complex numbers

Multiplication of complex numbers

Complex conjugate and the absolute value

Reciprocal of a complex number

Phasors

Chapter 3. Power, Intensity, and Decibels

Average power and RMS value

Crest factor

Decibels

Acoustics: pressure and intensity

Waves in time and space

* Lord Rayleigh

Measuring sound pressure levels

Adding signals

Spectral density and spectrum level

Observations on the decibel scale

A note on metric units of pressure

Chapter 4. Intensity and Loudness

Loudness level

Difference limens

Psychophysics

Intensity difference limens and loudness

* H. Fletcher

Loudness summation across frequency

Temporal integration

Chapter 5. Fourier Series

* J.B.J. Fourier

Definition of Fourier series

Projecting of functions

The spectrum

Symmetry

Computer evaluation of Fourier series coefficients

Chapter 6. Perception of Periodic Complex Tones

Musical tones and their sources

Harmonic analysis by the auditory periphery

Method: Pulsation threshold

Hearing out harmonics

Method: Bekesy tracking

Segregation and integration

Pitch and tone color

* G.S. Ohm

Pitch, chroma, and Shepard tones

Chapter 7. Delta Functions

Basic definition

Relation to the unit step function

Translation and selection properties

Application to Fourier transforms

Relation to the Kronecker delta

Further properties of the delta function

The lattice sum

Representations of the delta function

Chapter 8. The Fourier Integral

The transforms defined

Transforms of sine and cosine

Real functions, even and odd functions

Time shifting

Derivatives and integrals

Convolution

Introduction to correlation functions

Introduction to filtering

Periodic functions - Fourier series

Periodic functions and the lattice sum

Large and small scales

Fourier transforms of sgn and theta

Chapter 9. Filters

Filter fundamentals

The first-order filter

The second-order filter

The transversal filter

Dispersion relations

All-pass filters

Minimum-phase filters

Transfer function of the Hilbert transformer

Measuring transfer functions and coherence

Chapter 10. Auditory Filters

Cochlear tuning

Excitation patterns and critical bands

Critical bandwidth

* H.G. Barkhausen

The gammatone filter

The ubiquitous critical band

Chapter 11. Musical Measures of Frequency

Intervals

Dividing the octave

The unit of cents

Absolute musical scale

* H.L.F. von Helmholtz

Stretched and compressed tuning

Chapter 12. Pitch of Sine Tones

The definition of pitch

The dependence of pitch on intensity

Diplacusis, threshold microstructure, and emissions

Noise-induced pitch shift

Post-stimulatory pitch shift

Place theories and timing theories

* G. von Bekesy

The mel scale

The pitches of sines and complex tones

Chapter 13. Applications of the Fourier Transform

The energy spectrum and power spectrum

* S.S. Stevens

The alternating lattice

The forgetful Fourier transformer

The uncertainty principle

The spectral rake

Caveat on representations

Chapter 14. Correlation Functions and Spectra

The finite-duration signal autocorrelation function

The infinite-duration signal autocorrelation function

Autocorrelation for bands of noise

The symmetry of the autocorrelation function

Cross-correlation in three easy cases

The cross-spectrum

The Revcor technique

Autocorrelation and pitch perception

Chapter 15. Delay-and-Add Filtering

Impulse response and transfer function for delay and add

Repetition pitch

The comb filter

Delay-and-add filters in motion

Chapter 16. Probability Density Functions

Derivation of the PDF

PDF for the sum of two functions

PDF for random events

Averages and the PDF

Central moments

Chapter 17. Beats and Amplitude Modulation

Beats of equal-amplitude sines

Beats of sines with unequal amplitudes

Amplitude modulation

Balanced modulation

Beats and the frequency-domain grating

Chapter 18. The Envelope

Formal evaluation of the envelope

Envelope rules

Calculation of the envelope

The envelope and the Hilbert transform

* D. Hilbert

More envelope rules

The envelope and perception

Ensemble-average envelope

Chapter 19. Frequency Modulation

Narrow-band FM

Wide-band FM

The detection of frequency modulation

Chapter 20. Modulation Detection and Perception

Mixed modulation

Modulation detection and the critical band

FM and AM detection unified?

Masking by two tones

The modulation transfer function

Roughness

Chapter 21. Sampled Signals

The digitized signal

The sampled signal

The output signal

Sampling-jitter noise

The discrete Fourier transform

The fast Fourier transform

Oversampling

Chapter 22. Nonlinear Distortion

Memoryless representation

Dynamical representation

Harmonic distortion

Measurement of harmonic distortion

Intermodulation distortion

Distortion and audibility of phase

Auditory nonlinearity

Dynamic range compression

Chapter 23. Noise

Gaussian and thermal noise

Making noise

The power spectrum

The color of noise

Uniform exciting noise

* E.G. Wever

Noise fluctuations

Chapter 24. Signal Detection Theory

Two-alternative forced-choice

(M+1)-alternative forced-choice

Yes-No

* G.T. Fechner

Trials and procedures

Staircase methods

Efficiency

APPENDICES

A. Greek Alphabet

B. Trigonometric Functions

Definitions

Angle sum and difference formulas

Euler's formula and equivalents

C. Series

Infinite series

Binomial series

Geometric series

Special finite series

Special infinite series

D. Integrals - Even and Odd Functions

E. Integrals in the Complex Plane

Impulse response and the residue

Hilbert transform integrals

F. Hilbert Transform

Components of the analytic signal

Dispersion relations

Minimum-phase filters, gain and phase shift

G. Electrical Filters

H. The Normal Distribution

The error function

The cumulative normal

The central limit theorem

I. The Rayleigh Distribution

Generating random numbers having Gaussian and Rayleigh distributions

J. Standards

ISO frequencies

Mathematical constants

Units of pressure and hearing threshold

Physical constants

K. Calculation of Intermodulation Distortion

References

Index