## ECE403-2012AudioEngineering

• 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: 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: As in 2009; Syllabus: 2012; Assignments: See {$Daily Schedule$} below;

## Spring 2012 {$Daily Schedule$}

 L W D Date TOPIC 0 3 M 1/16 MLK Day; no class Part I: Linear Acoustics Systems (Theory) (12 lectures) 1 W 1/18 Introduction to what we will learn this semester. We will learn how a loudspeaker works, along with the basic theory needed to model this interesting and fun system.Review of ECE-210: Fourier {$\cal F$} and Laplace {$\cal L$} Transforms; Impedance {$Z(s)$} and other complex functions of complex frequency {$s$}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 1/20 1. Applications of the Laplace transform {$h(t) \leftrightarrow H(s)$} where {$t$} is time and {$s=\sigma+j\omega$} is complex-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 1/23 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 {${\cal L}^{-1}$}: {$f(t)u(t) = \int_{\sigma_0-j\infty}^{\sigma_0+j\infty} F(s)e^{st}\frac{ds}{2 \pi j}$} 4 W 1/25 3. 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.4. Using the Cauchy Integral Theorm to compute {${\cal L}^{-1}$} 5 F 1/27 5. 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) functions6. Detailed example using of a 1{$^{st}$}-order lowpass filter: the FT {$\equiv\cal F$} and Laplace Transform {$\equiv \cal L$}Homework 1: HW-1 Ver. 1.20 (due 2/10/2010) Come prepared to discuss and ask about the the problems you don't understand. 6 5 M 1/30 Allen out of town on business. 7 W 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: {$\delta((t))_R \leftrightarrow \frac{2\pi}{R} \delta((\omega))_{2\pi/R}$} 8 F 2/3 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 2/6 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 {$\delta(t) +\frac{j}{\pi t} \leftrightarrow 2 u(\omega)$} Homework 2: HW-2 (Ver 1.01) (due Mon 2/20/2010)Example of LaTeX (Hint: Try doing your HW using LaTeX!) 10 W 2/8 Review of Basic Acoustics (Pressure and Volume velocity, dB-SPL, etc.) 11 F 2/10 Class discussion of HW-2; FT; Acoustic wave equation. 12 7 M 2/13 Radiation (wave) impedance of a sphere; Acoustic Horns (pdf);Notes on the Laplace {$\delta(t)$} function (i.e., {$u(t) \equiv \int_{-\infty}^t\delta(t)dt$} it a function? (pdf) 13 W 2/15 Intensity, Energy, Power conservation, Parseval's Thm., Bode plots; Spectral Analysis and random variables: Resistor thermal noise (4kT). 14 F 2/17 Wave equations and Newton's Principia (July, 1687); d'Alembert solutions in 1 and 3 dimensions of the wave equation 15 8 M 2/20 HW2 Due; Review HW2; Review for Exam I; 16 W 2/22 No class due to: Exam I, 7-9PM Room: EVRT 245, Wed Feb 22, 2012 17 F 2/24 Review Exam solution; Transmission line Theory; Forward, backward and reflected traveling waves 18 9 M 2/27 2-port networks: Transformer, Gyrator and transmission lines (HW-3, HW-3-solution)(due 3/14/2010) Acoustic transmission lines 19 W 2/29 ; 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 20 F 3/2 Hunt 2-port impedance model of loudspeaker; Discussion of HW-3 21 10 M 3/5 Start Lab work on loudspeakers 22 W 3/7 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 3/9 No class - Engineering (Open House, UIUC Calendar) 23 F 3/9 Allen at AAS, Phonix AZ 24 11 M 3/12 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 3/14 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 3/15 Exam II, Thur @ 7 PM in 168 EL 26 F 3/16 No class (Exam II) - 12 Sa 3/17 Spring Break Begins - M 3/19 Spring Break - W 3/21 Spring Break - F 3/23 Spring Break 27 13 M 3/26 Transmission line Theory; reflections at junctions 28 W 3/28 Middle ear as a delay line Starter files for middle ear simulation: [Attach:ece403_txline.m Δ] [Attach:ece403_gamma.m Δ] 29 F 3/30 2-Port networks: Transmission line and RC network; T and Z forms 30 14 M 4/2 Measurement of 2-port RC example + demo of stimresp 31 W 4/4 2-port reciprocal and reversible networks (T and Z forms); HW-4 (due 4/14/2010) Measurement Circuit Schematic Δ 32 F 4/6 Throat and Radiation impedance of horn 33 15 M 4/9 2-port transducers and motional impedance (Hunt Chap. 2); Read Weece and Allen (2010) pdf 34 W 4/11 Loudspeakers: lumped parameter models, waves on diaphragm 35 F 4/13 Moving coil Loudspeaker I; 2-port equations with f = Bl i, E = Bl u 36 16 M 4/16 No class due to lab 37 4/18 No class due to lab 38 F 4/20 Guest Lecture: Lorr Kramer on Audio in Film 39 17 M 4/23 No class due to lab 40 W 4/25 Hand in early version of final paper on loudspeaker analysis 41 F 4/27 Guest Lecture: Malay Gupta (RIM): DSP Signal processing on the RIM platform 42 18 M 4/30 How a guitar works 43 W 5/2 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 5/4 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 DjVu versions. Either should work fine: traditional version and the open source version djview4 (recommended).