EECS 451 W04 Outline - Jeff Fessler
This list is based on what I covered in F98.
With luck, this list will be updated regularly over the course of the semester.
Course Text: Proakis and Manolakis, 3rd edition
Lecture# (x.x indicate sections from text)
1
Course Policies
1.1 terms
analog vs digital
1.2 classification of signals
1.3 frequency
1.4 a/d, sampling, quantization, d/a (brief)
2.1 discrete-time signals
representations
energy, power, periodicity, symmetry
2.6 cross-correlation, auto-correlation. skip: time-delay estimation
2
2.2 discrete-time systems
input-ouput relationship, block diagram
time properties: causality, memory, time invariance
amplitude properties: BIBO stability, invertibility, linearity
2.3 analysis
convolution
3
convolution properties
LTI properties in terms of impulse response
causality, invertibility, memory, stability
FIR vs IIR
4
2.4 difference equations
motivation for IIR
recursive implementation
2.5 implementation
applications (not in notes):
image edge detection, time-delay estimation
5
3.1 Z Transform
examples
ROC properties
6
3.2 Z transform properties
convolution, correlation, examples
7
more properties
3.3 rational z-transforms
pole zero plots
signal properties for real poles
8
signal properties for complex pole pair
system function for LTI by const. coef. diff. eq.
all zero, all pole, pole-zero
9
3.4 inversion of z transform
only mention contour integration
series expansion example
PFE
10
PFE example (impulse response)
4.5.7 digital sine-wave generator (2nd-order block diagram)
3.6.1 characterizing response of rational LTI systems
natural response, forced response
3.6.3 transient and steady-state response
11
3.6.4 stability
3.6.6 poles on unit circle
3.6.5 pole-zero cancellations
12
3.6.7 schur-cohn stability test (mention only)
Ch 4. Frequency Analysis
complex exponentials are eigenfunctions
family of Fourier transforms
Fourier series / power spectral density
13
4.2.1 DTFS, properties
4.4.3 periodic signals through LTI
14
DTFT
Inverse DTFT
2pi periodicity
DTFT vs Z
Convergence of DTFT
Gibbs phenomenon
4.2.5 energy density spectrum
Parseval's relation for DTFT
4.2.8 DTFT for periodic signals
15
exam1
16
4.3 DTFT properties
symmetry properties
DTFT properties continued
convolution property
4.2.12 dualities (Read!)
17
4.4 Frequency-domain char. of LTI systems
4.5 LTI systems as filters
4.5.x ideal filters
simple "treble boost" example
skip: 60Hz notch filter example (done in 206)
4.4.6 computing freq. response from pole-zero plot
18 (Yendiki)
4.2.9 sampling theorem
relations between DTFT and FT etc.
aliasing
bandlimited signals
sinc reconstruction
19 (Yendiki)
interpolation and applications
20
phase response from pole-zero plot
steady state, transient response (no, done already)
linear phase, group delay
4.5.2 simple lowpass filters
highpass from lowpass
digital resonators (bandpass) (brief)
21
4.5.6 all pass filters
4.6 inverse filters, deconvolution
minimum phase
4.5.7 generating sinusoids (no, done earlier)
22
linear phase
summary of DTFS, Z, frequency response, etc.
mid-term evaluations
23
A/D D/A upsampling, down-sampling example.
24
8.1 Digital filter design
causality and Paley-Wiener theorem
25
8.2 FIR linear phase causal filter design
delays / taps
26
8.2 FIR design using windows
8.2.2 FIR design by using windows
time-delay, sidelobes, transition band
27
8.2.3 FIR design by frequency sampling
8.2.4 FIR equiripple design
28
remez algorithm usage and tradeoffs
8.3 IIR filter design from analog filters
causal stable IIR filters cannot have linear phase
8.3.3 bilinear transformation
29
cheby1
use of practical filters before downsampling
bandpass
30
5. DFT overview
DFT introduction, examples
31
exam 2
32
Inverse DFT by coefficient matching
DFT of sinusoids
DTFT sampling
33
DTFT sampling example
periodic superposition, circular extension
time-limited signals
DFT, IDFT - computational perspective (skip)
5.2 DFT properties
linearity
circularly even sequence
circularly odd sequence
symmetry properties
34
review of transient response
35
5.2.2 convolution property
circular convolution
linear convolution via zero-padded DFT
36
5.2.3 other properties of DFT
shift properties
correlation
5.3.1 filtering with DFT's
5.3.2 filtering long sequences
37
DFT-based filtering by sampling H(omega)
5.4 freq. analysis of signals via DFT (fftshift)
38
upsampling/interpolation via DFT (interpft)
brief overview of discrete wavelet transform.
5.5 summary
39 (blatt)
6.1 FFT
radix 2
40 (blatt)
6.2 FFT methods
41
wavelets (for review of up/down sampling)
course evaluations
42
wavelets in freq. domain (more review)
over-sampled A/D and transition band
----------------- stuff i didn't have enough time to cover ----
2D DTFT
2D frequency response
2D filtering examples
2D DFT
Dolby application?
D/A zero-order hold / filter