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-frequency 2. 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. | |
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) functions | |
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$} images; 6 walls and arrays of images; simulation methods pdf Is a room minimum phase and thus invertable? djvu | |
20 | F | 3/2 | Hunt 2-port impedance model of loudspeaker; Discussion of HW-3 | |
21 | 10 | M | 3/5 | Start Lab work on loudspeakers |
22 | W | 3/7 | 2-Port networks; Definition and conversion between Z and T matrix; Examples, applications and meaning Carlin 5+1 postulates 5+1 Postulates,T and Z 2-ports | |
23 | F | 3/9 | No class - Engineering (Open House, UIUC Calendar) | |
23 | F | 3/9 | Allen at AAS, Phonix AZ | |
24 | 11 | M | 3/12 | Acoustic horns: Tube acoustics where the per-unit-length impedance {${\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 |
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