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 Date
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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 ECE210: 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 complexfrequency 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 {${\cal L}^{1}$}: {$f(t)u(t) = \int_{\sigma_0j\infty}^{\sigma_0+j\infty} F(s)e^{st}\frac{ds}{2 \pi j}$}

4

 W
 1/25

3. Definition of an impedance as an Analytic function Z(s): Must satisfy the CauchyRiemann 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: allpole (StrictlyIIR), allzero (StrictlyFIR) and allpass (AP) functions 6. Detailed example using of a 1{$^{st}$}order lowpass filter: the FT {$\equiv\cal F$} and Laplace Transform {$\equiv \cal L$} Homework 1: HW1 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.: {$\delta(t) \leftrightarrow 1$}, {$\delta(tT) \leftrightarrow e^{j\omega T}$}; {$1\leftrightarrow 2\pi\delta(\omega)$}, etc.] Periodic Functions: {$f((t))_R \equiv \sum_n f(tnR)$} 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 {$\sum_n \delta(tnR) \leftrightarrow \frac{2\pi}{R}\sum_k \delta(\omega k\frac{2\pi}{R})$} or in a a more compact form: {$ \delta((t))_R \leftrightarrow \frac{2\pi}{R} \delta((\omega))_{2\pi/R} $}

8

 F
 2/3

Shorttime Fourier Transform (STFT) AnalysisSynthesis: Let {$w(t)$} be lowpass 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: HW2 (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, dBSPL, etc.)

11

 F
 2/10
 Class discussion of HW2; 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, 79PM 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
 2port networks: Transformer, Gyrator and transmission lines (HW3, HW3solution) (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 2port impedance model of loudspeaker; Discussion of HW3

21
 10
 M
 3/5
 Start Lab work on loudspeakers

22

 W
 3/7
 2Port networks; Definition and conversion between Z and T matrix; Examples, applications and meaning Carlin 5+1 postulates 5+1 Postulates,T and Z 2ports

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 perunitlength 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
 2Port networks: Transmission line and RC network; T and Z forms

30
 14
 M
 4/2
 Measurement of 2port RC example + demo of stimresp

31

 W
 4/4
 2port reciprocal and reversible networks (T and Z forms); HW4 (due 4/14/2010) Measurement Circuit Schematic Δ

32

 F
 4/6
 Throat and Radiation impedance of horn

33
 15
 M
 4/9
 2port 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; 2port 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
