EE 351.3
Signals and Systems Assignment #1
Assigned: Due:
16 September 2010 23 September 2010
1.
Express the following complex numbers in the form ( x + jy ): a)
1 j e 2
b)
1 j e 2
c) e j
2
d) e j5
2
e)
2e j
4
2.
Express the following complex numbers in t
EE351Spectrum Analysis and Discrete Time Systems (Fall 2005)
SOLUTIONS
Solutions to Assignment 7
1. (Frequency Response or Transfer Function of an LTI System) Consider two signals x(t) and y(t) shown below.
x(t )
1
y (t )
1
-0.5 0
0.5
t (sec)
0
1
2
3
t (s
A
A
EE351Spectrum Analysis and Discrete Time Systems (Fall 2005) T t T T 0 0
T
t
SOLUTIONS
Solutions to Assignment 6
[7] 1. (Fourier Transform of u(t) Fourier transform of the DC signal is (). Fourier A u (t )
1
0
t
12
0
t
1 sign(t ) 2
1 exp(at ) 1 2 2
0
EE351Spectrum Analysis and Discrete Time Systems (Fall 2005)
SOLUTIONS
Solutions to Assignment 5
1. Consider the following discrete-time periodic signal: 2 2 x[n] = 1 + sin n + 3 cos n + cos 5 5 [2] [4] 4 n+ 5 2
(10)
(a) The fundamental period of x[n] is
EE351Spectrum Analysis and Discrete Time Systems (Fall 2005)
SOLUTIONS
Solutions to Assignment 1
[8] 1. (Signal Energy) Find the energies of the signals illustrated in Fig. 1. Comment on the eect on energy of sign change, time shifting, or doubling of the
EE351Spectrum Analysis and Discrete Time Systems (Fall 2005)
SOLUTIONS
Solutions to Assignment 4
1. Consider the continuous-time periodic signal: x(t) = 2 sin(2t 3) + sin(6t) [4] (8)
(a) Obviously, the fundamental frequency is 0 = 2. Using Eulers relation
EE351Spectrum Analysis and Discrete Time Systems (Fall 2005)
SOLUTIONS
Solutions to Assignment 2
1. (Linear and Time-Invariant Properties) Consider an LTI system whose response to the input signal x1 (t) in Figure 3-(a) is the signal y1 (t) illustrated in
EE351Spectrum Analysis and Discrete Time Systems (Fall 2005)
SOLUTIONS
Solutions to Assignment 3
1. Use the denition of the convolution integral to derive the following properties: [3] (a) Shifting:
x(t) (t t0 ) =
x( )(t t0 )d x(t t0 )(t t0 )d
=
= x(t
UNIVERSITY OF SASKATCHEWAN MIDTERM EXAMINATION
EE
Professor: Time: Notes:
351
Signals and Systems
Dr. D. M. Oct.22,2009 85 minutes Exam is closed book. 1 sheet (both sides) of formulas is allowed. All4 questions are of equal value.
Klymyshyn
1.
Short prob
EE 351.3
Signals and Systems Assignment #2
Assigned: Due:
30 September 2010 7 October 2010
The problems are from Ch. 2 of Signals and Systems (Oppenheim). Do ONLY the following parts:
2.1 a, b 2.10 a 2.21 d 2.22 b (dont sketch y(t), c (sketch y(t)
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EE351Spectrum Analysis and Discrete Time Systems
EXAMPLES
Convolution Integral Consider a continuous-time LTI system whose impulse response is h(t) = et u(t). Find and sketch the output of the system for the input signal x(t) shown in Fig. 1.
x(t) 1
h(t)