Introduction to Acoustics and Digital Signal Processing.
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Course Syllabus :
1. Introduction and overview
2. Mathematical preliminaries.
Logarithms, decibels and cents
Complex Analysis
Cartesian and polar form, Euler formula
functions of complex variables
differentiation and Cauchy-Riemann equations
integration, Cauchy theorem, residues, Laurent series
Fourier Transform and Fourier Series
FS as a special case of FT
FT as a special case of FS
Dirac delta-function
Complete Orthonormal Sets and Resolution of Identity
Convolution and Deconvolution
3. Basic Acoustics
Elementary Physics of Vibrations
Simple Harmonic Oscillator, damped and driven oscillations,
Resonance, Normal Modes
Elementary Physics of Waves
wave classification, wave propagation, Heisenberg
principle, transverse waves on a string
Elementary Physics of Sound
wave equation for sound, sound speed, sound intensity,
plane and spherical waves, sound radiation
4. Overview of Psychoacoustics
Hearing
elementary physiology of hearing, perception of musical
sound (intensity vs. loudness, frequency vs. pitch,
spectrum vs. timbre), transients
Production of Musical Sound
flues, reeds, string (plucked vs. bowed), percussion
Audio with computers: MIDI and Csound
Physics and Math of Consonance vs. Dissonance
Sound Reproduction and Room Acoustics
reverberation time: calculations and measurements
other room acoustics criteria
microphones and loudspeakers
electronic architecture
5. Signal Processing in Acoustics
Fundamentals of Signal Processing
convolution and correlation, Fourier transform,
the 5 fundamental theorems, Hilbert transform and
analytic signal, Schroeder Integrated Impulse
Determination of Impulse Response and Transfer Function
response to an impulse, response to a sine (stepped
or swept; Time Delay Spectroscopy), deconvolution
in frequency domain, flat-spectrum signal in the time
domain: Shift Register Sequences and Hadamard Transform
(with Spread-Spectrum applications)
Time-Frequency Distributions
the Sinusoidal Representation
Wigner distribution an its extensions
Field trip to measure the acoustics of a) the Physics Loading Dock
b) Walker Ames room
(incl. the Littlefield pipe organ demonstration,
and J.S.Bach's Triple Art of Fugue)
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The Laboratory Exercise (in the Physics of Music Lab, room B143):
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(sign-up sheet will be available in class; the lab takes about 2 hours).
Measure the impulse response and the transfer function of an electrical
circuit by the MLS method (using the CLIO system), and compare results
with directly exciting the circuit with a narrow pulse.