Learning Objectives for Final
Dror Baron
April 2016
The material for this test will focus on Chapters 4-8 and 10. That said,
this is a comprehensive exam and material from earlier chapters will also be covered.
In addition to skills required for the midterm, students should be able to
demonstrate the following specific skills:
1. Discuss when the Fourier transform of a signal is dened and in what senses (mean
square convergence and uniform convergence).
2. Apply dualities between dierent types of transforms (for aperiodic/periodic and con-
tinuous/discrete time signals) to simplify computations.
3. Partition a signal into odd/even and real/imaginary components when appropriate.
4. Apply properties of the Fourier transform.
5. Compute spectral characteristics of AM signals.
6. Evaluate how exponential and sinusoidal signals are processed by LTI systems.
7. Analyze the frequency response of difference equation systems.
8. Employ the geometric properties of how the pole zero plot affects the Fourier response
of a difference equation system to evaluate such systems qualitatively.
9. Design simple filters based on pole and zero placement.
10. Identify different types of filters (lowpass, bandpass, notch, etc.) based on their polezero
plots.
11. Relate between the spectral response of a continuous time signal and its sampled
discrete time counterpart.
12. Identify aliasing when it takes place.
13. Design a simple sampling, digital processing, and signal reconstruction system.
14. Familiar with basic concepts in implementation of D/A and A/D systems.
15. Utilize spectral properties of the periodic extension of a discrete time signal
and its relation to sampling of the Fourier transform of the original aperiodic signal.
16. Compute the discrete Fourier transform (DFT).
17. Invoke properties of the DFT in performing different computations.
18. Circular convolution: compute it in the time domain, frequency domain,
and employ its relation to DFT when convenient.
19. Perform linear convolution (including of long sequences) using the DFT.
20 Evaluate which windows (rectangular, Hamming, Hann, etc.) might be useful
for specific problems in frequency analysis and FIR filter design.
21. Understand the basics of divide and conquer algorithms such as the FFT.
22. Contrast different algorithms for computing the DFT.
23. Design FIR filters using windows.
24. Convert an analog filter to a digital one in order to design an infinite
impulse response (IIR) filter.
25. Most importantly, you will be able to use Matlab to solve various problems
involving previously mentioned learning objectives.
And here are some formalities:
1. You need to work out your solutions by hand and justify (explain) your answers.
2. While the WebWork homeworks were along the lines of “training” questions that familiarize
you with concepts, the final will have questions of different difficulty levels.
(See tests in previous years for examples.)
3. Open book; open handouts; open notes. Simple calculators will be allowed; communicating
devices will not.