Book: Signals, Sound, and Sensation

SIGNALS, SOUND, AND SENSATION

William M. Hartmann

Signals, Sound, and Sensation photo

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

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
  • 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

* Indicates Biography