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.

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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