ECE216: Signals & Systems
Quiz #3: Sections 07 & 08 (Tuesday)
Name:
Student Number:
You have 15 minutes to complete this quiz.
(Q1) When presented with the input x1 (t) = u(t) u(t 2), an LTI system produces the
output
t
0t<1
y1 (t) =
t + 2 1 t < 2
Sketch

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A continuous-timeystem's utput y(t) b relatedto its input r(t)by the equation
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.
Answer and justify dearly and conciselythe following questions.Is the

UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
Department of Electrical and Computer Engineering
ECE216S Signals and Systems
Mid-Term Examination, March 2006
Examiners: T. J. Lim, S. W. Davies, H. K. Lo.
Instructions:
Answer ALL questio

ECE216: Signals & Systems
Quiz #4: Sections 07 & 08 (Tuesday)
Name:
Student Number:
You have 20 minutes to complete this quiz.
(Q1) An LTI system has the impulse response h[n] = n u[n].
(a) Find its response to the input x[n] = n if |/ | < 1.
(3 marks)
(b

ECE216: Signals & Systems
Quiz #4: Sections 03 & 04 (Wednesday)
Name:
Student Number:
You have 20 minutes to complete this quiz.
(Q1) Suppose
1 n
u[n + 1]
2
h[n] = u[n + 2] u[n 3].
x [n ] =
Find y [n] = x[n] h[n], simplifying your answer as much as possib

ECE216: Signals & Systems
Quiz #4: Sections 01 & 02 (Friday)
Name:
Student Number:
You have 15 minutes to complete this quiz.
(Q1) An LTI system has the impulse response
h[n] = [n] + 0.5 [n 1] + 0.25 [n 2].
(a) Find the values of k for which h[n k ] = 0.

ECE216: Signals & Systems
Quiz #3: Sections 05 & 06 (Thursday)
Name:
Student Number:
You have 15 minutes to complete this quiz.
(Q1) Consider two systems with input-output equations as follows:
t
x( )d
S1 :
y (t) =
S2 :
y (t) = x(t 2).
(a) If S1 s output

ECE216: Signals & Systems
Quiz #3: Sections 03 & 04 (Wednesday)
Name:
Student Number:
You have 15 minutes to complete this quiz.
(Q1) A signal x[n] = u[n] u[n 3] is input to an LTI system with impulse response
h[n] = u[n] u[n 2].
(a) Find the system outpu

ECE216: Signals & Systems
Quiz #4: Sections 05 & 06 (Thursday)
Name:
Student Number:
You have 20 minutes to complete this quiz.
(Q1) Let
n, 0 n 4
and
0, otherwise,
h[n] = u[n 2] u[n 5].
x [n ] =
Sketch y [n] = x[n] h[n].
(5 marks)
Solution:
We have
h[n k