UNIVERSITY OF WATERLOO
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE 342 (Sections 1 & 2) Signals and Systems
Midterm Examination
Wendesday June 14, 2006, 5:30 pm - 7:00 pm
Instructors: L.-L. Xie and M. O. Damen
Time of exam: 5:30 pm
Duration of e
UNIVERSITY OF WATERLOO
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE 342 (Sections 1 & 2) Signals and Systems
Final Examination
Friday, August 11, 2006, 9:00 am - 11:30 am
Instructors: L.-L. Xie and M. O. Damen
Time of exam: 9:00 am
Duration of ex
Signals and Systems - ECE 342
August 11, 2010
Sample Final solutions
Question 3
Part (i)
Please see Final notes available online
Part (ii)
(D + 2)y(t) = x(t)
Lcfw_(D + 2)y(t) = Lcfw_x(t)
sY (s) y(0) + 2Y (s) = X(s)
Y (s)(s + 2) = X(s)
1
Y (s) =
X(s) = Yzs
ECE-342 Problem Set 6:Non_-Periodic Inputs and Fourier Transforms
1. The signal :1:(t) is band-limited by the angular frequency (.03, namely its Fourier transform X (w)
is such that
X(w)=0, forallewB,
and is the input to the ideal low-pass ﬁlter with tran
ECE-342 Problem Set 3: Frequency Domain Analysis of Continuous Time Systems
1. Determine £{z(t)} (s) for the signal
2:(t) = [1, 3](t).
2. Determine the inverse Laplace transform for
sz+3s+7
X(s) = [(s + 2)2 + 4](s + l)-
3. Determine the inverse Laplace tr
ECE-342 Problem Set 6:Non_-Periodic Inputs and Fourier Transforms
1. The signal :1:(t) is band-limited by the angular frequency (.03, namely its Fourier transform X (w)
is such that
X(w)=0, forallewB,
and is the input to the ideal low-pass ﬁlter with tran
EOE-342 Problem Set 1: Introduction to Signals and Systems
1. Find the energy in the following signals:
(a) 3(t) = 2[u(t —- 1) — u(t — 2)]
(b) $(t) = t[u(t) - u(t - 5)]
(c) 14k] = (%)ku[k— 3].
2. Find the average power in the following signals:
(a) w) = u
EOE-342 Problem Set 2: Time Domain Analysis of Continuous Time Systems
1. In the circuit of Fig. 1 the input signal is the current i,(t), and the output signal is the voltage
v(t).
Fig. 1
Determine the differential equation relating i,(t) with v(t).
2.
EOE-342 Problem Set 5:Periodic Inputs and Fourier Series
1. Determine the exponential Fourier coefﬁcients for the signal
2:(t) = 1 + sin(wot) + 2 cos(wot) + cos(2wot + 7r/4)L
2. The input to an LTI system with impulse response
h(t) = e"u(t)
is the periodi