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Name (Last, First) Student ID number UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering Electrical Engineering and Computer Sciences Department EECS 145M: Microcomputer Interfacing Laboratory Spring Midterm #2 (Closed book- equation sheet provided- calculators OK) Wednesday, April 21, 2004 PROBLEM 1 (16 points) 1a (8 points) When periodically sampling a waveform, what causes frequency aliasing and how can it be avoided? 1b (8 points) When periodically sampling a waveform and computing its Fourier transform, what causes spectral leakage and how can it be avoided?
PROBLEM 2 (25 points) Design a Butterworth anti-aliasing low pass filter that meets the following requirements:
- Gain > 0.99 for frequencies below 20 kHz
- Gain < 0.01 for frequencies that alias below 20 kHz
- The sampling frequency is 80 kHz
- The filter has the minimum number of components (lowest order)
3d. (15 points) List the hardware and software steps necessary to sample the data, to determine the frequency values, and to determine relative amplitudes. 3e. (5 points) Would your system work if f 1 = 3000 Hz and f 2 = 3001 Hz? If not, how could you modify your procedure to determine these frequencies?
Problem 4 (24 points) Power lines operate at 60 Hz, but distortion of the harmonic waveform caused by inductive loads can introduce a 180 Hz component that is harmful to transformers. Design a system for using a computer (equipped as in problem 3) and digital filtering to continually monitor the amplitude of the unwanted 180 Hz component of the power line waveform. Assume that you continuously sample the 115 volt AC power line at 180 x 1024 Hz = 184,320 Hz. 4a. (12 points) List the hardware and software steps necessary to sample the data, to continually compute the 180 Hz amplitude using a finite impulse response digital filter, and to continually print the amplitude to the computer screen.
