L
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 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 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
 1/25
 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 {${\cal L}^{1}$}: {$f(t)u(t) = \int_{\sigma_0j\infty}^{\sigma_0+j\infty} F(s)e^{st}\frac{ds}{2 \pi j}$} 3. Definition of an Analytic function F(s): Must satisfy the CauchyRiemann 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), allpole (StrictlyIIR), allzero (StrictlyFIR) 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, Bilinearz, etc.; HW1 (due 2/10/2010)

5

 F
 1/29

Class discussion of HW1 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.: {$\delta(t) \leftrightarrow 1$}, {$\delta(tT) \leftrightarrow e^{j\omega T}$}; {$1\leftrightarrow 2\pi\delta(\omega)$}, 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} $}

7

 W
 2/3

Class canceled and Replaced by: iOptics seminar (121) 1000 MNTL (Abstract Δ) free Pizza!

8

 F
 2/5

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
 2/8
 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, dBSPL, etc.); HW2 (due 2/24/2010); Example of LaTeX (Hint: Try doing your HW using LaTeX!)

11

 F
 2/12

Class discussion of HW2
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 79PM 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
 2port networks and transmission lines;HW3 (due 3/17/2010) Acoustic transmission lines

20

 F
 3/5
 Discussion of HW3

21
 10
 M
 3/8
 Gaines Hall, guest lecture on Concert Hall (NPI) acoustics.

22

 W
 3/10
 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
 3/12
 No class  Engineering Open House

24
 11
 M
 3/15
 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
 3/17
 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
 2Port networks: Transmission line and RC network; T and Z forms

30
 14
 M
 4/5
 Measurement of 2port RC example + demo of stimresp

31

 W
 4/7
 2port reciprocal and reversible networks (T and Z forms); HW4 (due 4/14/2010) Measurement Circuit Schematic Δ

32

 F
 4/9
 Throat and Radiation impedance of horn

33
 15
 M
 4/12
 2port 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; 2port 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
