 ## ECE403-2010AudioEngineering

• Instructor: Jont Allen (NetID: jontalle); ECE 403 Websites: 2010, 2009; 2008; Time-table: UIUC-ECE403; Text: Electroacoustics (Buy, TOC, Preface,Preface1, djvu); Office hours: 2-3 Friday (following class)
• Topics: acoustic wave phenomena; acoustics of rooms and auditoriums; artificial reverberation and sound localization/spatialization; Transducer design (2-port networks, loudspeakers, microphones); Topics in digital audio.
• Goals: As in 2009; Syllabus: 2009; Assignments: See {$\sqrt{-Daily Schedule}$} below;

## Spring 2010 {$\sqrt{-Daily Schedule}$}

 L W D Date TOPIC 0 3 M 1/18 MLK Day; no class Part I: Linear Acoustics Systems Theory (12 lectures) 1 W 1/20 Introduction; Review Fourier Trans. {$\cal F$} and the Laplace Trans. {$\cal L$}; A detailed comparison of the step function {$u(t)$} for each transform: Why {${\cal F} u(t) =\pi \delta(\omega)+1/j\omega$} and {${\cal L} u(t)=1/s$} are not the same. The strange case of {$\log(-1)$},{$j^j$}, {$(-1)^t$} and {$j^t$} 2 F 1/22 1. Applications of the Laplace transform {$h(t) \leftrightarrow H(s)$} where {$t$} is time and {$s=\sigma+j\omega$} is frequency2. Convolution of vectors {$\leftrightarrow$} product of polynomials: {$a \star b \leftrightarrow A(z)\cdot B(z)$}, where {$a \equiv [a_0,a_1,a_2, \cdots]^T$}, {$b \equiv [b_0,b_1, \cdots]^T$} and {$A(z)\equiv(a_0+a_1z+a_2z^2 \cdots)$}, {$B(z)\equiv(b_0+b_1z+ \cdots)$}3. Functions of a complex variable: The calculus of Analytic functions {$dH(s)/ds$}, {$\int_C H(s) ds$}. 3 4 M 1/25 1. Solving differential equations: The characteristic polynomial {$H(s)$}2. Properties of {$H(s)=N(s)/D(s)$}: Roots of {$D(s)$} in LHP.3. Definition of the Inverse Laplace transform {${\cal L}^{-1}$}: {$f(t)u(t) = \int_{\sigma_0-j\infty}^{\sigma_0+j\infty} F(s)e^{st}\frac{ds}{2 \pi j}$}3. Definition of an Analytic function F(s): Must satisfy the Cauchy-Riemann conditions, assuring that {$dF/ds$} and {$\int_C F(s) ds$} (e.g. {${\cal L}^{-1}$}) are defined.4. Using the Cauchy Integral Theorm to compute {${\cal L}^{-1}$}5. Special classes of impulse responses: Minimum phase (MP), positive real (PR), all-pole (Strictly-IIR), all-zero (Strictly-FIR) and allpass (AP) functions 4 W 1/27 6. Detailed example using of a 1{$^{st}$}-order lowpass filter: the FT {$\equiv\cal F$}, zT, Laplace Transform {$\equiv \cal L$}, DFT, Bilinear-z, etc.; HW-1 (due 2/10/2010) 5 F 1/29 Class discussion of HW-1 Come prepared to discuss and ask about the the problems you don't understand. 6 5 M 2/1 Review of the Fourier Transform [e.g.: {$\delta(t) \leftrightarrow 1$}, {$\delta(t-T) \leftrightarrow e^{-j\omega T}$}; {$1\leftrightarrow 2\pi\delta(\omega)$}, etc.]Periodic Functions: {$f((t))_R \equiv \sum_n f(t-nR)$} with {$n \in \mathbb{Z}$} and their Fourier Series {$f((t))_R = \sum_k f_k e^{jt 2 \pi k/R}$}; Sampling and the Poisson Sum formula {$\sum_n \delta(t-nR) \leftrightarrow \frac{2\pi}{R}\sum_k \delta(\omega- k\frac{2\pi}{R})$} or in a a more compact form: {$\delta((t))_R \leftrightarrow \frac{2\pi}{R} \delta((\omega))_{2\pi/R}$} 7 W 2/3 Class canceled and Replaced by: iOptics seminar (12-1) 1000 MNTL (Abstract Δ) free Pizza! 8 F 2/5 Short-time Fourier Transform (STFT) Analysis-Synthesis: Let {$w(t)$} be low-pass with {${2\pi\over R} > \omega_{\mbox{\tiny cutoff}}$}, normalize such that: {$W(0) = \int w(t) dt = R/2\pi$}. Then {$w(t)\ast\delta((t))_R = w((t))_R \approx 1 \leftrightarrow \frac{2\pi}{R} W(\omega)\cdot \delta((\omega))_{2\pi/R} \approx 2\pi \delta(\omega)$} (pdf Δ) 9 6 M 2/8 More on Fourier Transform analysis; Hilbert Transform and Cepstral analysis as applications of {$u(t) \leftrightarrow \pi\delta(\omega)+{1 \over j\omega}$} and its Dual {$\delta(t) +\frac{j}{\pi t} \leftrightarrow 2 u(\omega)$} 10 W 2/10 Review of Basic Acoustics (Pressure and Volume velocity, dB-SPL, etc.); HW-2 (due 2/24/2010); Example of LaTeX (Hint: Try doing your HW using LaTeX!) 11 F 2/12 Class discussion of HW-2 FT; STFT; Acoustics 12 7 M 2/15 Wave equations and Newton's Principia (July, 1687); d'Alembert solutions in 1 and 3 dimensions of the wave equation; Radiation (wave) impedance of a sphere; Acoustic Horns; 13 W 2/17 Intensity, Energy, Power conservation, Parseval's Thm., Bode plots; Spectral Analysis and random variables: Resistor thermal noise 14 F 2/19 Review for Exam I 15 8 M 2/22 No class due to Exam I; Exam I 7-9PM Room 245EL Monday Feb 22, 2010 16 W 2/24 Review Exam solution; 17 F 2/26 Transmission line Theory; Forward, backward and reflected traveling waves; Room acoustics I: 1 wall = 1 image, 2 walls = {$\infty$} images 18 9 M 3/1 Room Acoustics II: 6 walls and arrays of images; simulation methods pdf Is a room minimum phase and thus invertable? djvu 19 W 3/3 2-port networks and transmission lines;HW-3 (due 3/17/2010) Acoustic transmission lines 20 F 3/5 Discussion of HW-3 21 10 M 3/8 Gaines Hall, guest lecture on Concert Hall (NPI) acoustics. 22 W 3/10 2-Port networks; Definition and conversion between Z and T matrix; Examples, applications and meaningCarlin 5+1 postulates 5+1 Postulates,T and Z 2-ports 23 F 3/12 No class - Engineering Open House 24 11 M 3/15 Acoustic horns: Tube acoustics where the per-unit-length impedance {${\cal Z}(x,s)\equiv s \rho_0/A(x)$} and admittance {${\cal Y}(x,s)\equiv s A(x)/\eta_0 P_0$} depend on space {$x$}Radiation impedance pdf Δ; Transmission Line discussion 25 W 3/17 History of Acoustics, Part I;History of acoustics (Hunt Ch. 1)Newton's speed of sound; Lagrange & Laplace+adiabatic history Review material for Exam II; Discussion of final project on Loudspeaker measurements: pdf 11 Th 3/18 Exam II, Thur @ 7 PM in 260 EL 26 F 3/19 No class (Exam II) - 12 M 3/22 Spring Break - W 3/24 Spring Break - F 3/26 Spring Break 27 13 M 3/29 Transmission line Theory; reflections at junctions 28 W 3/31 Middle ear as a delay line Starter files for middle ear simulation: [Attach:ece403_txline.m Δ] [Attach:ece403_gamma.m Δ] 29 F 4/2 2-Port networks: Transmission line and RC network; T and Z forms 30 14 M 4/5 Measurement of 2-port RC example + demo of stimresp 31 W 4/7 2-port reciprocal and reversible networks (T and Z forms); HW-4 (due 4/14/2010) Measurement Circuit Schematic Δ 32 F 4/9 Throat and Radiation impedance of horn 33 15 M 4/12 2-port transducers and motional impedance (Hunt Chap. 2); Read Weece and Allen (2010) pdf 34 W 4/14 Loudspeakers: lumped parameter models, waves on diaphragm 35 F 4/16 Moving coil Loudspeaker I; 2-port equations with f = Bl i, E = Bl u 36 M 4/19 No class due to lab 37 W 4/21 No class due to lab 38 F 4/23 Guest Lecture: Lorr Kramer on Audio in Film 39 17 M 4/26 No class due to lab 40 W 4/28 Hand in early version of final paper on loudspeaker analysis 41 F 4/30 Guest Lecture: Malay Gupta (RIM): DSP Signal processing on the RIM platform 42 18 M 5/3 How a guitar works 43 W 5/5 Last day of class; Review of what we learned; discussion of how loudspeakers work (what you found) Tr 5/6 Reading Day; Final project due by midnight: Please give me both a paper and pdf copy. NO DOC files - F 5/7 Final Exams begin Not proofed beyond here

## Textbook

• The textbook is Electroacoustics: The Analysis of Transduction, and Its Historical Background by Frederick V. Hunt. ISBN 0-88318-401-X.
• Chapters 2 and 3 of the textbook are available here.
• You will need the DjVu viewer to read/print it. This can be found at:
viewer.
there are two versions, and either should work fine: the traditional version and the open source version djview4 (recommended).