520.214 Signals and Systems Self Test
1. What is the polar form of the complex number 1 + j ?
(a) 1
(b) 2 ej
(c) 2 ej/4
(d) 2 ej/2
(e) None of the above.
2. What is the polar form of the complex number 1 j ?
(a) 2 ej/4
(b) 2 ej/4
(c) 1
(d) 2 ej/2
(e) None
1. Consider the true statement: If A then B.
(a) What is the contrapositive of this statement?
(b) What is the converse of this statement?
(0) Use truth tables to determine if the converse is equivalent to the original state
ment.
8 sir/A 4 _?
003 l? not
Spring 2016
520.214 - Signals and Systems
Homework 4 - SOLUTIONS
Assigned 3/29/16, Due 4/12/16
* PLEASE write down your section number on your homework copy
Section 1 : Wednesday
Section 2 : Monday
Problem 1:
Suppose x(t) is periodic with fundamental peri
Spring 2016
520.214 - Signals and Systems
Homework 3 - SOLUTIONS
Assigned 3/3/16, Due 3/24/16
* PLEASE write down your section number on your homework copy
Section 1 : Wednesday
Section 2 : Monday
Problem 1: Compute the convolution y[n] = x[n] h[n] of the
Spring 2016
520.214 - Signals and Systems
Homework 1 - SOLUTIONS
Assigned 2/4/15, Due 2/18/15
* PLEASE write down your section number on your homework copy
Section 1 : Wednesday
Section 2 : Monday
Problem 1: Compute the rectangular form of the complex num
Spring 2016
520.214 - Signals and Systems
Homework 2
Assigned 2/18/16, Due 3/3/16
* PLEASE write down your section number on your homework copy
Section 1 : Wednesday
Section 2 : Monday
Problem 1:
System S1 takes as input x1 [n] and yields output y1 [n].
S
Spring 2016
520.214 - Signals and Systems
Homework 5
Assigned 4/14/16, Due 4/28/16
* PLEASE write down your section number on your homework copy
Section 1 : Wednesday
Section 2 : Monday
Problem 1:
Determine the Fourier series coefficients for each of the
Spring 2016
520.214 - Signals and Systems
Homework 3
Assigned 3/3/16, Due 3/24/16
* PLEASE write down your section number on your homework copy
Section 1 : Wednesday
Section 2 : Monday
Problem 1: Compute the convolution y[n] = x[n] h[n] of the following p
Spring 2016
520.214 - Signals and Systems
Homework 5 - SOLUTIONS
Assigned 4/14/16, Due 4/28/16
* PLEASE write down your section number on your homework copy
Section 1 : Wednesday
Section 2 : Monday
Problem 1:
Determine the Fourier series coefficients for
Spring 2016
520.214 - Signals and Systems
Homework 4
Assigned 3/29/16, Due 4/12/16
* PLEASE write down your section number on your homework copy
Section 1 : Wednesday
Section 2 : Monday
Problem 1:
Suppose x(t) is periodic with fundamental period T0 and Fo
Spring 2016
520.214 - Signals and Systems
Homework 1
Assigned 2/4/15, Due 2/18/15
* PLEASE write down your section number on your homework copy
Section 1 : Wednesday
Section 2 : Monday
Problem 1: Compute the rectangular form of the complex numbers:
9
(a)
Recitation problem Set 8
1. Compute y(t) = (h x)(t) where
x(t)
h(t)
1
1
t
t
0
0
1
Graphically y(t) =
1
h( )x(t )d
x(t)
1
0
t2
t1
t
h()
1
0
1
For t 1 < 0 i.e. t < 1
y(t) = 0
no overlap
1
2
For t 2 > 1 i.e. t > 3
y(t) = 0
no overlap
For 0 t 1 1
1t2
i.e.
t1
520:214: Recitation Problem Set 3
1. For the LTI system with
h[n]
1
1
0
2
n
compute the responses (convolution) to the inputs:
(a) x[n] = u[n] A : y[n] = [n]
(b) x[n] = r[n] A : y[n] = u[n 1]
This system is called a rst dierence.
2. Is the LTI system with
520:214: Recitation Problem Set 2
1. Write z = ej/2 + j 2ej/4 in rectangular form and in polar form.
A: z = 1 + 2j,
|z| =
5,
z = tan1 (2/ 1) +
, so z =
1
5ej( tan
(2)+)
(The approximation to the angle is not required!)
2. Suppose the even part and odd pa
Recitation 7
1. A C-T system with input x(t) and output y(t) is characterised as follows:
y(t) 0 e(t ) x( )d for t 0. Is it memoryless? Causal? Linear?
It is not memoryless since at time t we need to integrate values of x( ) for
[0, ).
It is not causal s
Recitation problem Set 10
1. An LTI system with frequency response function
1 + j
1 + j
H() =
has a periodic input signal x(t). The fundamental period of x(t) is To = 2 and
the magnitude spectrum of x(t) is shown below.
|xk|
1
1/2
.
.
4
3
2
1
2
1
k
4
3
Sk
Spring 2016
520.214 - Signals and Systems
Homework 2 - SOLUTIONS
Assigned 2/18/16, Due 3/3/16
* PLEASE write down your section number on your homework copy
Section 1 : Wednesday
Section 2 : Monday
Problem 1:
System S1 takes as input x1 (t) and yields outp