# Book: Signals, Sound, and Sensation

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

The list price is \$80.

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
• 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
• 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

• Impulse response and transfer function for delay and add
• Repetition pitch
• The comb filter

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?
• 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

* Indicates Biography