EE445S Real-Time Digital Signal Processing Laboratory - Midterm #2

Prof. Brian L. Evans

Each midterm exam will be an open book, open notes, open laptop exam that is scheduled to last the entire period. The laptop must have all external networking connections disabled.

Midterm #1 for the spring 2018 semester will be on Monday, May 4th, during lecture time (11:00 am to 11:50 am) but in ECJ 1.214 that seats 83. ECJ 1.214 has tables (continuous writing surfaces). With 25 students in the class, you should have at least two empty seats or an aisle on either side of you. The extra space will help you be more comfortable to arrange your books, notes, and laptop for the midterm exam.

About 70% of Midterm #2 will come from lecture, and the remainder will come from lab. The problem(s) relating to the lab may require you to write C code.

The class average on midterm #2 has varied semester to semester. Before the curve, the class average has been typically around 60.

Here are several example midterm #2 exams with and without solutions:

These and other previous midterm #2 exams are available in the course reader.

Coverage of midterm #2 includes the material presented in lecture and lab since the first midterm. Much of the material covered since the first midterm builds on material from before the first midterm.

For Midterm #2, you will be responsible for the material in

  1. Lectures 7-8, 12-16 and 26. Lecture 26 is review for midterm #2.
  2. In-class discussions
  3. Johnson, Sethares, and Klein, Software Receiver Design, sections 6.5-6.7, sections 7.1-7.2, chapters 8-9, sections 10.1-10.4, chapter 11, sections 12.1-12.3, sections 13.1-13.3, sections 16.1-16.5, and appendices A, D, E, and F
  4. Welch, Wright and Morrow, Real-Time Digital Signal Processing, chapters 10 and 16-18, and appendices A-D
  5. Laboratory assignments 4-7
  6. All handouts in the course reader, esp. Raised Cosine Pulse, Modulation Summary, Noise-Shaped Feedback Coding, Direct Sequence Spreading, Symbol Synchronization, Communication Performance of PAM vs. QAM, and Adding Random Variables
  7. Homework assignments 4-7 and their solution sets (in addition, homework assignments 0-3 and their solution sets will also be helpful)
  8. Simon Haykin, Communication Systems, excerpts on "Random Modeling", from Sections 4.6 Random Processes, 4.8 Mean, Correlation and Covariance, 4.9 Ergodicity, 4.10 Transmission of a Random Process Through a Linear Filter, 4.11 Power Spectral Density, and 4.12 Gaussian Process.
For Midterm #2, you will be responsible for the following topics:
  1. Interpolation: pulse shapes, oversampling, and design tradeoffs (lecture 7)
  2. Quantization: system properties, SNR vs. bits of resolution, noise floor, power spectra, and design tradeoffs for A/D converters (lecture 8)
  3. Pseudo noise sequences and their applications (lab 4)
  4. Data conversion (lecture 10): dithering, oversampling, and noise shaping. Example problems
  5. Channel impairments (lecture 12) including linear time-invariant, linear time-varying, and nonlinear distortion as well as additive noise
  6. Matched Filtering (lecture 13) including pulse shaping, matched filtering, channel equalization and noise analysis
  7. Digital PAM, including error analysis, power requirements, transmission, and reception (lecture 14 and lab 5)
  8. Digital QAM, including error analysis, power requirements, transmission, and reception (lectures 15 and 16, and lab 6)
Topics from lectures 10-11, 17-25 and 27 that were not covered in class will not be covered on midterm #2: Nonetheless, the content in these lecture slides may be helpful in preparing for an interview for a company that makes programmable DSPs or heavily uses programmable DSPs in its products.

In preparing for midterm #2, I would recommend working through the problems on the midterm #2 tests in the course reader, starting with the most recent midterm #2 tests. I would also recommend thoroughly understanding the solution sets for homework assignments 0-7.

For the Fall 2003 midterm #2, you can ignore the first problem, as we haven't covered the topic of analog phase modulation.

Here are calculations on midterm #2 that I have seen a few students have difficulty getting right:

  1. Complex number calculations. Let z = r exp(j w):
  2. Polynomial factoring and expansion
  3. Based on our discussion of all-pass filters in lecture 6, one way to stabilize a discrete-time IIR filter is to reflect its poles that are outside the unit circle to be inside the unit circle. That is, for each pole p = r exp(j w) for which r > 1, change the pole to be pnew = (1/r) exp(j w). The magnitude response is preserved, but the phase response will change. (Note that poles on the unit circle remain unchanged, which means that filters with a repeated pole on the unit circle would remain unstable.) In the context of designing all-pass filters, poles are obtained by reflecting the zero locations inside the unit circle.
  4. Decision regions for a constellation tell the receiver how to apply thresholds to a sampled output of the matched filter to decide which symbol (constellation point) was most likely sent. The decisions regions must cover the entire real line for PAM, and the entire plane for QAM.

Updated 01/31/18.