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