 ## ECE403-2013AudioEngineering

• Instructor: Jont Allen (NetID: jontalle); ECE 403 Websites: 2013, 2012, 2011,2010, 2009; 2008; Time-table: UIUC-ECE403; Text: Electroacoustics (Buy, TOC, Preface, Preface1, djvu);
• TA: Noori Kim (nkim13@illinois.edu); Office hours: Wednesday 12:00-1:00PM, 260 Everitt Lab; Allen Office hours: 2-3 Friday (after lab)
• Calendars: Class, University; Time, place, etc. official
• Topics: How to analyize a loudspeaker; 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, Syllabus: 2013; Assignments: See {$Daily Schedule$} below;Software: G7 software
• This week's schedule

## Spring 2013 {$Daily Schedule$}

 L W D Date TOPIC Part I: 1-port Network Theory (5 Lectures: L1-4,6; 1 Labs: L5) 1 3 M 1/14 *Introduction to what you will learn this semester: You will understand how a loudspeaker works by learning the basic theory along with hands-on lab experiments.*Everyone will work in a small group (ideally 4 students per group).*Theory will be taught on Monday and Wed, while the Labs will be on Friday.*Review of ECE-210: Fourier {$\cal F$} and Laplace {$\cal L$} Transforms; Impedance {$Z(s)$} and other complex functions of complex frequency {$s$}*The Curious Case of {$\log(-1)$},{$j^j$}, {$(-1)^t$} and {$j^t$} 2 W 1/16 *Applications of the Laplace transform {$h(t) \leftrightarrow H(s)$} where {$t$} is time and {$s=\sigma+j\omega$} is complex-frequency*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. *Impedance; Analytic functions;*Functions of a complex variable: The calculus of Analytic functions {$dH(s)/ds$}, {$\int_C H(s) ds$}.*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 F 1/18 *Solving differential equations: The characteristic polynomial {$H(s)$}*Properties of {$H(s)=N(s)/D(s)$}: Roots of {$D(s)$} in LHP.*Definition of the Inverse Laplace transform {${\cal L}^{-1}$}: {$f(t)u(t) = \int_{\sigma_0-j\infty}^{\sigma_0+j\infty} F(s)e^{st}\frac{ds}{2 \pi j}$}*Homework 1: HWa (due 1/28/2010) 0 4 M 1/21 MLK Day; no class 4 W 1/23 *Definition of an impedance as an Analytic function {$Z(s)$}: Must satisfy the Cauchy-Riemann conditions, assuring that {$dZ/ds$} and {$\int_C Z(s) ds$} (e.g. {${\cal L}^{-1}$}) are defined.*By using the Residue Thm, and the Cauchy Integral Theorm, one may compute {${\cal L}^{-1}$} 5 F 1/25 First Lab: 251EL (your iCard should get you into the lab) *Set up groups; learn about hardware 6 5 M 1/28 *Special classes of impedance functions as: Minimum phase (MP), positive real (PR), and transfer functions as: all-pole (Strictly-IIR), all-zero (Strictly-FIR) and allpass (AP) functions*Detailed example using of a 1{$^{st}$}-order lowpass filter via the Laplace Transform {$\equiv \cal L$} In the future, move HWb (Lab Exercise) here, or swap HWc with HWb 2-port Linear System Theory (4 lectures: L7,9-12, 2 Labs: L8,L11) 7 W 1/30 *2-Port networks; Definition of T [Pipes (53)] matrix and conversion method between Z and T matrix [Van Valkenburg (65)] (pdf, djvu) 8 F 2/1 Second lab (251EL) *Setup of hardware; Learn how to make impedance measurements: Circuit Schematic Δ *Calibration of hardware 9 6 M 2/4 *Terminology (How do you know if you have learned something? Can you explain a complex concept, given a defining word?)*Hunt's 2-port impedance model of the loudspeaker*Carlin 5+1 network postulates (pdf, djvu)*Homework 2 (Lab exercise) HWb (due: Wed, Feb 13, 2013) 10 W 2/6 *2-port networks: Transformer, Gyrator and transmission lines *Moving coil Loudspeaker I; 2-port equations with f = Bl i, E = Bl u 11 F 2/8 No class due to lab *Measurement of 2-port RC example + demo of stimresp *Homework 3: HWc (due Mon Feb 20, 2013)*Example of LaTeX (Hint: Try doing your HW using LaTeX!) 12 7 M 2/11 *2-port transducers: motional impedance (Hunt Chap. 2); Read Kim and Allen (2013) pdf*The Maxwell Faraday Law in differential and integral form Exam I should appear in Week 12, following Lecture 7 Acoustic Transmission Line Theory (5 lectures L13,15-16,18-19; 2 Labs: L14,17; Exam I: L20) 13 W 2/13 *Uniform Transmission line; reflections at junctions *Forward, backward and reflected traveling waves*Reciprocal and reversible 2-port networks (T and Z forms) 14 F 2/15 *No class due to lab *First measurement of a loudspeaker input impedance 15 8 M 2/18 *Review of Acoustic Basic Acoustics (Pressure and Volume velocity, dB-SPL, etc.) 16 W 2/20 *Acoustic Intensity, Energy, Power conservation, Parseval's Thm., Bode plots;*Spectral Analysis and random variables: Resistor thermal noise (4kT). HWc Due Today. *Move HWd here in the future 17 F 2/22 No class due to lab 18 9 M 2/25 Review for Exam I, Lectures 1-12 19 W 2/27 No class due to: Exam I, 7-9PM Room: EVRT 241, Wed Feb 27, 2013 20 F 3/1 *Lab Part II: Waves and Horns (3 lectures L22,25-26,28; 2 Labs: L23-24; Exam II: L27) 21 10 M 3/4 *Acoustic wave equation.*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 {$x$} (Horns);HWd: Transmission Lines (due Mon, Mar 11, 2013) 22 W 3/6 *Spherical wave off of a sphere*Radiation (wave) impedance of a sphere*Wave equations and Newton's Principia (July, 1687); d'Alembert solutions in 1 and 3 dimensions of the wave equation 23 FS 3/8-9 Regular Lab 251EL; Engineering (Open House, UIUC Calendar) 24 11 M 3/11 *Radiation impedance of a Horn pdf Δ*Transmission Line discussion*Loudspeakers: lumped parameter models, waves on diaphragm *Throat and Radiation impedance of horn *In the future, HWd should be assigned here 25 W 3/13 *Guest speaker Jack Buser; Senior Director, PlayStation Digital Platforms Sony Computer Entertainment America*jack_buser@playstation.sony.com 26 Th 3/14 Exam II, Thur @ 7 PM in EVRT 241 F 3/15 No class (Exam II) 12 M-F 3/18-22 Spring Break 27 13 M 3/25 *Lecture: How does the middle ear work?*HWe due April 8, 2013; Starter files for middle ear simulation (txline.m Δ,gamma.m Δ); Similar to HW3 of ECE537 Part III: Signal Processing (3 lectures L27,29-30; 2 Labs: L28,31;) 28 W 3/27 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.]*Notes on the Laplace {$\delta(t)$} function (i.e., {$u(t) \equiv \int_{-\infty}^t\delta(t)dt$} it a function? pdf) 29 F 3/29 No class due to lab 30 14 M 4/1 *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: {$\delta((t))_R \leftrightarrow \frac{2\pi}{R} \delta((\omega))_{2\pi/R}$} 31 Marcelo W 4/3 *One-sided FTs: Hilbert Transform {$u(t) \leftrightarrow \pi\delta(\omega)+{1 \over j\omega}$} and its Dual {$\delta(t) +\frac{j}{\pi t} \leftrightarrow 2 u(\omega)$}* Cepstral analysis and its applications to Speech processing 32 F 4/5 No class due to lab Part III: Hearing and Hearing Aids (5 lectures L27,29-30,32-33; 2 Labs: L28,31,34;) 33 15 M 4/8 * Lecture: Middle ear as a delay line *Read Rosowski, Carney, Peak (1988) The radiation impedance of the external ear of cat: Measurements and applications (pdf)HWe due 34 W 4/10 *The intensity JND and Loudness: Weber's, Fechner's and Steven's Laws; Brain Image 35 F 4/12 Final lab 36 16 M 4/15 *How does a microphone work?; Sigma-Delta 24 bit oversampled with noise shaping analog to digital converters: A light-weight overview. 37 W 4/17 *Noori Kim Lecture: Modeling a hearing aid (ear bud) receiver 38 F 4/19 *Guest Lecture: Lorr Kramer on Audio in Film Part IV: Selected Topics (5 lectures L38-40,42-43, 1 Lab: 41) 39 17 M 4/22 *History of Acoustics, Part II;History of acoustics History & (Hunt Ch. 1) *Newton's speed of sound; Lagrange & Laplace+adiabatic history*Discussion of your final project on Loudspeaker measurements: Content, format, style, grading (ECE403 project) 40 W 4/24 *Lecture Final summary of how a loudspeaker work 41 F 4/26 Ryan group presentation 42 18 M 4/29 *Austin group presentation*Steven group presentation*Hand in preliminary version of final paper on loudspeaker analysis 43 W 5/1 *Group 4 presentation (Marcelo)*Room acoustics: 1 wall = 1 image, 2 walls = {$\infty$} images; 6 walls and arrays of images; simulation methods pdf; Is a room minimum phase and thus invertable? djvu Tr 5/2 Reading Day; Final project due by midnight: Please give me both a paper and pdf copy. NO DOC files - F 5/3 Final Exams begin (Our final is the Lab project paper on loudspeakers) Not fully 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 DjVu versions. Either should work fine: traditional version and the open source version djview4 (recommended).