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:

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

The list price is $80.


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

Chapter 3. Power, Intensity, and Decibels

Average power and RMS value
Crest factor
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
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
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
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

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

Chapter 21. Sampled Signals

The digitized signal
The sampled signal
The output signal
Sampling-jitter noise
The discrete Fourier transform
The fast Fourier transform

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
* G.T. Fechner
Trials and procedures
Staircase methods

A. Greek Alphabet
B. Trigonometric Functions

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


* Indicates Biography