ECSE-4760
REAL-TIME APPLICATIONS IN CONTROL & COMMUNICATIONS
Name _________________________
Exam #1
(open notes, calc., no laptops)
Answer all questions (both sides)
Spring 2015
Section: MR 1:30_X
(25 pt)
1. On the lab PC system with ±10 volt 12-bit 2's complement converters, for the given input sawtooth wave, a
program performs a logical bitwise OR with 0x0400 then a logical bitwise XOR with 0x0800 on the samples before
outputting them to the DAC. Sketch the expected resultant output waveform on the same axis (ignoring
processing delays). Indicate the voltage values at the most positive and most negative peaks of the output
signal with 12-bit accuracy. Note the input voltage range.
(4 pt)
2. Which architecture(s) have 2 or more data paths (for instructions or data) to the processor from memory for faster
execution?
a) Microcontrollers b) CISC processors c) RISC processors
d) DSP
e) None of these
(6 pt)
3. How many address and data lines would a LUT need to multiply 2 positive integers whose values range from 0 to
500?
(4 pt)
4. TRUE or FALSE: A switched capacitor filter may require a D/A conversion on the output signal.
(4 pt)
5. Given an oversampling Sigma-Delta system sampling at 500kHz, what must the minimum 1-bit voltage resolution be
to keep up with an input ramp rising (briefly) at 100V/s?
(5 pt)
6. A 10-bit shaft encoder is on the end of a threaded rod that has 20 threads/inch (20 rotations to move 1 inch). What
fraction of an inch will an object move if the encoder value changes by 10 counts?
(6 pt)
7. Name the kind of error is displayed in the plot to the right and give one of the
possible sources for the error in the converter system.
(6 pt)
8. A 0-10V dual-slope converter takes 0.2ms to convert when the input is 2V and 0.3ms to convert when the input is 4V.
How long would it take to convert when the input is 8V?
Given the following digital filter simulation diagram with a sample frequency of 80k radians/s, answer questions 9 – 15.
5/8
x(k)
∑
z1
(3 pt)
9. What is the sample period T?
z1
5/8
∑
y(k)
-1/4
(8 pt)
10. What is the transfer function H(z)?
(12 pt)
11. Find the frequency(ies) where |H(z)| = 1.
1
0
k
H
z
o
(5 pt)
13. Draw the Pole-Zero diagram for H(z) & indicate where f = 0Hz,
f = fs/4, and f = fs/2.
(2 pt)
12. Find the Gain at f = 10kHz.
(2 pt)
14. Classify the stability of this system (Stable, Marginally Stable, or Unstable).
(2 pt)
15. If every ‘z’ in the transfer function were changed to an ‘s’, how would the system be classified in the Laplace domain?
16. The FARES.vi program show cases where undersampling causes ambiguity. Discrete video frames at 30 fps (frames
per second) in a movie of a spinning wheel may cause the appearance that the wheel is turning much slower or even
in reverse due to “aliasing”. If the frame rate is 6 times faster than the spin, a wheel with 6 evenly spaced spokes will
appear to be stationary in the video due to the frame rate capturing partial rotation at a repeating point in the pattern.
(Think of old western movies with wagon wheels.)
(3 pts)
a) If the wheel spins at exactly 10 Hz (10 revolutions/s) clockwise and the camera is at 30 fps, will the wheel appear to
be spinning at any speed on the video display?
(3 pts)
b) If the wheel rotational speed increases to 11 Hz will the video image make the wheel appear to be moving clockwise
or counterclockwise?