ECE 316 Midterm Exam
Spring 2015
Name _________________________________
A. Multiple Choices (30 points, 3 points / problem, only one correct answer)
1. Laplace transform is a generalization of ( A )
A. Fourier transform
B. Z-transform
C. DTFT
D. DFT
2. Suppose that two cascade-connect LTI systems have transfer functions
H(s) and G(s). Then, what is the overall transfer function? ( D )
A. H(s)+G(s)
B. H(s)/G(s)
C. H(s)-G(s)
D. H(s)G(s)
3. Which one is a pole of
A.
B.
C.
D.
( B )
2
3
1
16
4. Which of the following is the region of convergence (ROC) of a right-sided
sequence in the z-transform? ( A )
A. Outside of a circle
B. Inside of a circle
C. Outside of a square
D. Inside of a square
5. The zero-pole diagram of a discrete-time LTI system is given below.
Which type of filter does the system belong to? ( B )
A.
B.
C.
D.
High pass
Low pass
Band pass
Band stop
6. To
realize
a
discrete
time
system
with
transfer
function
, what is the minimum number of delay units needed?
(B )
A. 1
B. 2
C. 3
D. 4
7. Suppose the continuous time signal has the maximum frequency 10kHz,
what is the Nyquist rate? ( C )
A. 5kHz
B. 10kHz
C. 20kHz
D. 40kHz
8. To sample a bandlimited periodic signal without information loss, how
many samples are needed? ( B )
A. Infinitely many
B. Finitely many
C. Hard to say
D. A single sample
9. For a band limited continuous-time signal, if we sample with exactly the
Nyquist rate, what will happen? ( B )
A. There is no information loss if the signal is sinusoidal.
B. We cannot uniquely determine the original continuous time signal.
C. We can recover the original signal by using an ideal low pass filter.
D. We can recover the original signal even if we use a limited time
window.
10. What is the common feature of DTFT and DFT? ( A )
A. Discrete time
B. Discrete frequency
C. Continuous time
D. Continuous frequency
B. Laplace Transform (25 points)
Find the time-domain function that is the inverse Laplace transform of the following
function:
hint: check whether this is left-sided or right-sided sequence?
C. Z-transform (25 points)
Consider
(input) is
a
causal discrete-time LTI system with transfer function
. Find out the time-domain response (output) when the excitation
.
Hint: you can calculate the z-transform X(z). The output of the LTI system has a
z-transform X(z)H(z). Then, do the inverse z-transform to obtain the time
domain response.
D. Sampling (20 points)
Consider the following sinusoidal signal with the fundamental frequency f0 of
4kHz:
.
(1) The signal is sampled at a sampling rate of 6000 samples/s and
reconstructed with an ideal low pass filter with the following transfer
function:
Determine the reconstructed signal.
(2) Repeat (1) for a sampling rate of 12000 samples/s and an ideal low pass
filter with the following transfer function:
hint: find the spectrum of the impulse sampled signal; then figure out the
output of the filters.