EE445S Real-Time Digital Signal Processing Laboratory - Midterm #1

Midterm #1 will be an open book, open notes exam scheduled to last the entire period. Midterm #1 questions will come from lecture and lab. It is possible that one problem on the midterm may require you to write TMS320C6700 C/assembly code. TMS320C6700 assembly language instructions are tabulated in the slides for lectures 2 and 9.

Here are several example midterm #1 exams:

• Spring 2014 without solutions and with solutions
• Fall 2013 without solutions and with solutions
• Spring 2013 without solutions and with solutions

For Midterm #1, you will be responsible for the material in

1. In-class lectures 0-6 and lecture 9
2. In-class demonstrations, including those from DSP First. Username and password information.
3. In-class discussions
4. Johnson, Sethares and Klein, Software Receiver Design, chapters 1-7 and appendices A & G
5. Welch, Wright and Morrow, Real-Time Digital Signal Processing, chapters 1-7 and appendices A-D
6. Laboratory assignments 1-3
7. Handouts in the course reader entitled Convolution Example, Fundamental Theorem of Linear Systems, Modulation Example, Sample Quizzes, Tapped Delay Line on C6700 DSP, and All-pass Filters
8. Homework assignments 0-3 and their solution sets

For Midterm #1, you will be responsible for the following topics:

1. Communication system introduction (Lecture 0)
2. Conventional programmable digital signal processor architectures (Lecture 1)
3. Bandwidth (Lecture 2)
4. Sinusoidal generation (Lecture 2)
5. Upconversion and downconversion (Lectures 2 and 4)
6. Continuous-time system properties (Lecture 3)
7. Basic continuous-time signals (Lecture 3)
8. Discrete-time system properties (Lecture 3)
9. Basic discrete-time signals (Lecture 3 and 5)
10. Fundamental Theorem of Linear Systems for continuous-time systems (Handout F)
11. Sampling theorem (Lecture 4)
12. Sampling and aliasing (Lecture 4
13. Bandpass sampling (Lecture 4)
14. Discrete-to-continuous conversion (Lecture 4)
15. Fundamental Theorem of Linear Systems for discrete-time systems (Lecture 5)
16. Z-transforms (Lecture 5 and 6; Johnson & Sethares Appendix A.4)
17. Transfer functions (Lecture 5 and 6; Johnson & Sethares 4.5)
18. Relationships between transforms (Lecture 5)
19. Digital FIR filter implementation (Lecture 2 and 5)
20. Digital FIR filter analysis (Lecture 5)
21. Stability of continuous-time and discrete-time filters (Lecture 5 and 6)
22. Digital IIR filter design by pole-zero placement (Lecture 6)
23. Three direct form IIR filter structures (Lecture 6)
24. Classical IIR filter design methods (Lecture 6)
25. Implementing IIR filters in cascade of biquads based on quality factors (Lecture 6)
26. Modern programmable digital signal processor architectures (Lecture 9)

Here are examples of calculations that many students have had trouble getting right on midterm #1.

The first common mistake is deriving transfer functions. One source is Lathi's Linear Systems and Signals book, which uses the operator notation D y(t) to represent (d/dt) y(t) or y'(t). This is not an error. Lathi's book continues as follows, given input signal x(t) and output signal y(t):

y'(t) + y(t) = x(t)
D y(t) + y(t) = x(t)

(D + 1) y(t) = x(t)

y(t)     1
---- = -----
x(t)   D + 1
       y(t)
h(t) = ----
       x(t)

Comments:

• Clearly, h(t) = y(t) / x(t) is not a meaningful way to represent a system, and moreover, it isn't valid for values of t when x(t) is zero.
• h(t) should have been the impulse responses of an LTI system-- a differential equation with initial conditions is only an LTI system if the initial conditions are zero. In that case,

  y(t) = h(t) * x(t)
  

  where * means convolution.
• Transfer functions are derived in either the generalized transform domain (i.e. Laplace or z) or the Fourier domain. The transfer function in the Fourier domain is also known as the frequency response. There is no concept of a transfer function in the time domain.