EE502: Digital Filters
Topics and Notes Summary (updated frequently):
|Friday, May 2||Last class day. Research project reports are due!
Concluding lecture comments: 4-D, data compression, etc.
|Wednesday, Apr. 30||Student project summaries (Jerry Gregoire, et al.?) this day.
Lecture: Extension of 2-D to multiple dimensions: space-time (4-D) signal concepts.
|Monday, Apr. 28||Guest Lecture by James D. Johnston, Microsoft Corp., on perceptual audio coding.
|Friday, Apr. 25||Continued discussion of 2-D signal processing, circular convolution, and recursive filters.|
|Wednesday, Apr. 23||Guest lecture by Chip Lukes covering his DSP MS thesis project.
|Monday, Apr. 21||2-D signal processing: frequency response, 2-D DFT, and intro to FIR filters.|
|Friday, Apr. 18||No class this day (University holiday)
|Wednesday, Apr. 16||Complete adaptive signal processing discussion and begin image processing (2-D signal processing) overview.|
|Monday, Apr. 14||Review an example of the LMS adaptive procedure. Discuss convergence and adaptation rate issues.|
|Friday, Apr. 11||Continue coverage of simple adaptive structures and the LMS algorithm.
Here is a Matlab script for a simple adaptive interference canceler, and a few plots showing the response behavior.
Students should have identified and received approval for the research project topics by this date.
|Wednesday, Apr. 9||Complete the discussion of the STFT by considering synthesis process.
Begin material on adaptive signal processing and the LMS algorithm.
|Monday, Apr. 7||Returned Exam #2 papers. Scores ranged from the high 20s to the high 30s out of 48.
Assigned Research Projects (due on last day of class, Friday, May 2).
Presented some applications of the STFT, including spectral analysis and gap extrapolation.
|Friday, Apr. 4||Exam #2 (in class)|
|Wednesday, Apr. 2||Developed short-time Fourier transform description and math. Discussed use of the STFT for time-variant spectral analysis.|
|Monday, Mar. 31||Reminder: the second exam will be given in class on Friday, April 4. Coverage includes
topics since the first exam, with particular emphasis on noise shaping, coefficient
rounding, quantization, and overflow.
Continued review of DFT windows, and began discussion of short-time Fourier transform (STFT).
|Friday, Mar. 28||Began Chapter 10 material on using the DFT for spectral analysis. Commented on the time-frequency resolution tradeoff and the effects of the analysis window.|
|Wednesday, Mar. 26||Continued DCT discussion. Handed back HW#4 and commented on several of the problems.
ASSIGNMENT #5 Due Friday, April 4, at start of class. Assignment handout.
|Monday, Mar. 24||Completed discussion of FFT basics (handout slides). Began description of discrete
cosine transform (DCT) from the end of Chapter 8.
|Friday, Mar. 21||Reminder: homework is due at the start of class.
Covered the overlap-add and overlap-save techniques for implementing LTI systems using the DFT and IDFT. There will be a homework problem on this next week.
Began review of the decimation-in-time fast Fourier transform (FFT) decomposition. Web-based notes are available: FFT intro .
|Wednesday, Mar. 19||Finished presentation on real-time DSP systems. Began discussion of the discrete
Fourier transform (DFT) based on the material from Chapter 8. NOTE that there will
be a future homework problem involving filter design (Chapter 7), but we will not
cover that topic in the lectures for this course.
|Monday, Mar. 17||Presented some overhead transparencies describing several commercial DSP chip architectures
and features of real-time DSP systems. This material is for your information only:
I will not include this on the next exam.
Introduction to real time DSP and the Motorola 56300
|Mar. 10-14||Spring Break (no classes this week)
|Friday, Mar. 7||Looked at transfer function criteria to prevent or limit the likelihood of overflow,
and the resulting tradeoffs due to scaling the input signal. Reviewed several rules
of thumb for decomposing higher order structures into scaled second order sections.
Also mentioned the use of floating point to largely eliminate overflow issues--but
still need to consider coefficient quantization and roundoff. [End of Chapter 6 material]
ASSIGNMENT #4 Due Friday, March 21 at start of class.
|Wednesday, Mar. 5||Reviewed issues related to roundoff in digital filter structures (section 6.8). Calculated roundoff noise power at system output for direct form I system, assuming independent uncorrelated roundoff noise sources. Began talking about overflow issues.|
|Monday, Mar. 3||Talked about data time alignment in simulation problem from HW#3: must keep track
of time delays and shifts when doing sample-to-sample error calculations.
Looked at example of 3-bit coefficient quantization and available pole locations for a simple second-order complex conjugate pole system. Compared direct form structure to coupled form structure.
|Friday, Feb. 28||Returned and discussed exams (results were generally quite good). Collected homework
assignment #3, and discussed briefly the simulation problem.
Discussion of numerical issues and coefficient quantization effects (sections 6.6 and 6.7). Described 2's complement fixed-point fraction number representations.
|Wednesday, Feb. 26||Mid-Term Exam
The exam will cover material from chapters 2 through 4 in the textbook. The topics will be chosen primarily from the coverage of the homework problems, as well as from areas of emphasis in the lectures. It is expected that you will be able to identify poles and zeros, ROC and corresponding sequence characteristics, frequency response, magnitude and phase, demonstrate knowledge of LTI system behavior, and understand sample rate conversion topics. This exam will not include noise shaping.
The exam will be 50 minutes in duration during the normal class meeting time. You may bring and use your textbook and notes (but no consultants).
|Monday, Feb. 24||Review Direct Form I and Direct Form II, discuss decomposition into 2nd-order sections
(products) using a cascade, decomposition via partial fractions to implement a parallel
(sum) structure, and reversal of flow diagram branches to get a transpose structure.
|Friday, Feb. 21||Complete all-pass discussion from chapter 5, then start consideration of implementation
forms for LTI systems (chapter 6).
REMINDER: the first midterm exam will be held during class time on Wednesday, Feb. 26.
|Wednesday, Feb. 19||Introduced details of simulation problem. Discussed geometrical interpretation of
magnitude and phase based on pole and zero vectors (chapter 5).
ASSIGNMENT #3 NOW DUE Friday, Feb. 28 at start of class:
From textbook: 4.52; AND simulation problem.
|Monday, Feb. 17||No class (MSU Presidents' Day Holiday: campus offices open but no classes).
|Friday, Feb. 14||Homework #2 due at start of class.
Finish discussion of noise shaping and begin LTI magnitude and phase presentation.
|Wednesday, Feb 12||Considered the effect of oversampling on the signal-to-noise ratio: quantization
noise is spread over entire band, while signal is concentrated in pass band. LPF
removes noise that is in rejection band. Also began discussion of noise shaping.
|Monday, Feb. 10||Presented the mid-tread quantizer and the "linear model" of quantization as an additive
random noise. Emphasized that the "linear" noise model is not really correct, since
the quantization noise is typically correlated to some degree with the input signal
and seldom truly white. Nonetheless, the additive noise model can be helpful for
|Friday, Feb. 7||Returned homework #1 and a set of solutions. Discussed problems 2.25 and 3.44, since
there were several misunderstandings about these.
Reviewed computational inefficiency of filtering prior to downsampling (or after upsampling) because filter must be calculated at higher data rate. Presented "polyphase" implementation for reduced computational complexity. Next topics: quantization models and oversampling.
|Wednesday, Feb. 5||Completed discussion of the effects of downsampling and upsampling by integer factors,
and the use of an upsampler/downsampler cascade to perform sample rate conversion
by an integer ratio.
|Monday, Feb. 3||Considered the topic of digital sample rate conversion, starting with downsampling
(decimation) by an integer factor (section 4.6)
ASSIGNMENT #2 Due Friday, Feb. 14 at start of class:
From textbook: 4.3; 4.15; 4.21; 4.22; and 4.60; AND simulation problem.
|Friday, Jan. 31||Homework #1 due at start of class.
Determination of Fourier transform of sampled signal from the FT of the continuous time signal. Determination of relationship between Fourier transform of original signal and the DTFT of the sampled sequence. Bandlimited reconstruction via ideal lowpass--sinc interpolation (section 4.3).
|Wednesday, Jan. 29||Inverse z-transforms via inspection. Examples of partial fraction expansion (section
3.3). Quick discussion of the z-transform properties (section 3.4). Began description
of ideal impulse (Dirac) sampling function (chapter 4).
|Monday, Jan. 27||Considered region of convergence (ROC) characteristics of z-transforms (sections 3.1
NOTE: the solutions in the back of the book for two of the assigned problems may be in error in your textbook, depending on which printing/revision you have.
Problem 2.2 (a) N4 = N0 + N2, N5 = N1 + N3. (b) At most (N + M - 1) non-zero points.
Problem 2.7 (a) Periodic, N=12. (b) Periodic, N=8. (c) NOT periodic. (d) NOT periodic.
|Friday, Jan. 24||Completed discussion of chapter 2 (through section 2.9, not including 2.10 at this
time. Started consideration of z-transforms. Made comments regarding Fourier transform
(continuous - continuous), Discrete-time Fourier transform (discrete - continuous),
Discrete Fourier series (continuous - discrete), and Discrete Fourier Transform (discrete
|Wednesday, Jan. 22||Continuing discussion of material from chapter 2, up to section 2.6.
ASSIGNMENT #1 Due Friday, Jan. 31 at start of class:
From textbook: 2.2, 2.7, 2.25, 2.27, 2.35, 2.49, 2.70; 3.2, 3.9, 3.24, 3.32, 3.44
|Monday, Jan. 20||Reminder: Martin Luther King, Jr., holiday (no classes at MSU)
|Friday, Jan. 17||Discussion of material from chapter 2 of the textbook: discrete-time signals, notation,
and terminology. Pre-test results from Wednesday were discussed briefly--generally
students did OK.
ASSIGNMENT: Read chapter 2, sections 2.0-2.9.
|Wednesday, Jan. 15||First class meeting: review of syllabus, comments on course topics. A pre-test was given in order to ascertain the familiarity of the students with the basic course topics.|