ECSE-4760
REAL-TIME APPLICATIONS IN CONTROL & COMMUNICATIONS
Name __________________________
Exam #1
(open notes, calc., no laptops)
Answer all questions (both sides)
Spring 2014
Section: MR 1:30__
(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 does an integer multiply by 2 (with possible overflow) and then performs a logical AND with 0xFFFC 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.
7.5V
5.0V
2.5V
0.0
-2.5
-5.0
-7.5
(8 pts)
2. A digital sampling system with ideal reconstruction (using an ideal LPF) has fs = 25kHz and H(z) = 1. For input x(t) =
cos(2πft) with f = 125kHz, what is the frequency of the output cosine wave?. (Note aliasing.)
What is the largest the sampling frequency can be for the output frequency to be 25kHz? (Aliased, input still 125kHz)
(4 pts)
3. TRUE or FALSE: A custom hardwired IC has the best chance for achieving the highest fs sample frequency for a
digital filtering system.
(4 pts)
4. Which can achieve a higher sampling rate: a 4th order fixed-point DSP with 3 data buses or a 4th order switched
capacitor filter?
(4 pts)
5. Why can oversampling 1-bit Delta-Sigma converter systems use low-order low pass reconstruction filters?
(5 pts)
6. An ideal 0-5V 4-stage multipass subranging ADC design has 8 comparators. How many bits of resolution does this
ADC have?
(6 pts)
7. A low frequency 20Vp-p triangle wave is digitized and the samples sent to the DAC on the lab’s NI LabVIEW system.
If the input is set to 30Vp-p will the output look the same as if the original 20Vp-p signal’s samples were multiplied by
1.5 and sent to the DAC? Explain why or why not.
(3 pts)
8. Which kind of analog conversion error is displayed in the plot to the right?
(Circle the correct answer.)
Integral Nonlinearity Differential Nonlinearity Gain Offset Slope
9.
Given the following pole zero diagram and the peak of |H(z)| is at 2.5kHz
with unity gain at that frequency:
(1 pt)
a. What is the sample period, T
(4 pt)
b. What is the magnitude of the output for input 2sin(fst) where fs is the sample frequency?
(6 pts)
c. Find H(z).
0.5 x
o
-1
o
1
-0.5 x
(6 pts)
d. Find the backwards difference equation for output y(k).
(4 pts)
e. Draw the block diagram with gain, delay, and summing elements.
(3 pts)
f. What type of filter is this (LP, HP, BP, BS)?
(8 pts)
g. Set up the equation to find the frequency(ies) where the gain is down by 3dB from the peak. (No abs value in eqn.)
(9 pts)
9. Where must the poles be located for a digital filter to have its output only dependent on the inputs (current and
previous values) and NOT previous outputs?