ECSE-4760
REAL-TIME APPLICATIONS IN CONTROL & COMMUNICATIONS
Name __________________________
Exam #1
(open notes, no laptops)
Answer all questions (both sides)
Spring 2011
Section: MR 1:30__
MR 6:30__
(25 pts)
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 AND with 0x07FF on the samples and then shifts the value left one bit (with possible overflow)
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.
(8 pts)
2. A linear distance measurement system is to be designed using a megnetostrictive rod 5m long. The speed of sound
in the rod is 3000m/s. The time of flight is measured by counting pulses of a 5MHz clock. How many bits will the time
counter need to measure the round trip time the full 5m length of the rod?
(3pts extra credit) What is the resolution of the system in µm?
(4 pts)
3. TRUE or FALSE: A transcendental function such as exponentiation if implemented in software would be
approximately 150 times slower than a hardware implementation.
(5 pts)
4. TRUE or FALSE: All discrete time filters require the use of an ADC and DAC to input & output filtered analog signals.
(5 pts)
5. An ideal 0-5V 16-bit multipass subranging ADC design gets 4 bits each pass. What is the largest voltage that will
enter the last pass?
(5 pts)
6. For the ADC in 5., how many comparators would the complete system require?
(6 pts)
7. What is a major difference in the architecture of a DSP that permits high order filters to be implemented with very
high sampling frequencies compared to a von Neumann processor?
8.
Given a filter (with non-unity D.C. gain)
H1 (z) 
(z  23  j 12 )(z  23  j 12 )
(z  43  j 14 )(z  43  j 14 )
(4 pt)
a. Sketch the pole-zero diagram.

(3 pts)
b. Which best describes this filter: LPF, HPF, BPF, or BSF (BRF)?
(9 pts)
c. Find the difference equation relating the output y(k) to the input x(k) and any previous values.
(6 pts)
d. Draw the block diagram with gain (show values), delay, and summing elements.
(6 pts)
e. For a sampling frequency fs of 100kHz, at what frequency is the output amplitude minimized and at what frequency
is it maximized?
(3 pts)
f. What is the D.C. gain of the system?
(6 pts)
g. If H1(z) is followed by
H2 (z) 
z 2  32 z  58
, find HTOT(z), the reduced transfer function of the combined systems?
z 2  3z 1

(5 pts)
h. What is a practical issue (problem) in implementing H2(z)?