Introduction to Acoustics and Digital Signal Processing. -------------------------------------------------------- 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) -------------------------------------------------- The Laboratory Exercise (in the Physics of Music Lab, room B143): ----------------------- (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.