UNIVERSITY OF CALIFORNIA
College of Engineering
Electrical Engineering and Computer Sciences Department
145M Microcomputer Interfacing Lab
Final Exam Solutions May 18, 1992
1A Nyquist Theorem: To recover a waveform from its sampled values, the highest frequency
present must < one-half the sampling frequency.
1B Discrete Fourier Transform: Transform for determining the amplitude of the frequency
components of a periodically sampled waveform.
1C Differential Linearity Error (of an A/D converter): Difference between the spacing of neigh-
boring transition voltages and their average spacing. [4 points off if step size or transition volt-
age not mentioned] [4 points off if absolute or relative accuracy was defined]
1D Anti-Aliasing Filter: Low-pass filter used to block frequencies above one-half the sampling
frequency and thereby prevent aliasing.
1E Power Amplifier: Amplifier having high power or current output, and required to drive an
actuator such as a speaker or heater. [2 points off if high power or current output not
mentioned]
1F Digital Filter: Filter whose output is a linear combination of previous input and output values.
2A 110V (rms)
156V (p-p)
60 Hz
15R
R
Low Pass Filter
fc ≈ 4 kHz
Data
acquisition
circuit
Micro-
computer
Screen
display
Disk
Keyboard
data
data
ready
≈10V p-p
[3 points off if 156 V p-p sent directly into acquisition circuit]
[3 points off if low-pass filter omitted]
2B ∆f = 0.01 Hz, S = 1/∆f = 100 sec, N = 100 sec x 10 kHz = 106 samples
(S = 50 sec, N = 5 x 105 samples also acceptable)
2C F0 corresponds to 0 Hz or dc.
2D 60 Hz corresponds to F6000 and FN-6000 where N = 106
2E Since the distortion has a period of 60 Hz, only multiples of 60 Hz will be present.
The highest harmonic nmax that can pass the anti-aliasing filter is ≈ 5000 Hz/ 60Hz ≈ 80.
The nth harmonic will be at F6000n and F N – 6000n
[3 points off if only frequencies given]
[6 points off if only F6000 and FN– 6000 given]
[6 points off if answer says that all Fourier amplitudes are non-zero]
2F 1) Data acquisition circuit samples waveform, digitizes, and sets data ready line
2) When program detects data ready line, it reads data, stores data, and resets data ready line
3) Loop back to step 1 until 106 values taken
4) Multiply values by Hanning window
5) Compute the FFT
[2 points off for each step missing]
145M Final Exam Solutions (B) page 1 May 18, 1992 S. Derenzo/L. Bushnell
