18-290 Signals And Systems
Homework 6 solutions
Spring 2012
1. Let x(t) and y(t) both be continuous periodic signals having period T and with Fourier series representations given by:
ak ejk0 t
x(t) =
18-290 Signals And Systems
Homework 1
Issued: Friday, January 20, 2012
Spring 2012
Total Points: 20
Due: Thursday, January 26, 2012 (in class)
Note: Please solve the problems using only paper and penc
18-290 Signals and Systems
Spring 2017
Homework 4 Solutions
1. Consider sketches of 3 signals below:
b(t)
1
W
1
2W
t
t
-W
r(t)
b(t)*b(t)
2W
-2W
2W
-2W
-1
Sketch (a) b(t) r(t) and (b) r(t) r(t).
(Solut
18-290 Signals and Systems
Spring 2017
Homework 6 Solutions
1. You learned about Parsevals theorem in class:
Z
Z
1
2
|x(t)| dt =
|X(j)|2 d
2
This relationship is important because the left side repr
18-290 Signals and Systems
Spring 2017
Homework 1 Solutions
1. Let a, b > 0. Let
x(t) = eat u(t),
h(t) = ebt u(t).
Derive an expression of x(t) h(t).
Solution:
Z
x(t) h(t) =
x( )h(t )d
Z =
=
ea u( )eb
18-290
Signals and Systems
Profs. Aswin Sankaranarayanan and Richard Stern
Spring 2017
Homework 1 Solutions
1. A continuous-time signal x(t) is periodic if x(t) = x(t T ) for all t. The fundamental
pe
18-290 Signals and Systems
Spring 2017
Homework 1 Solutions
1. Derive, from the defining equations, the Fourier transform of the following signal.
x(t) = teat u(t),
Hint:
R
t (1+t)
tet dt = e
2
a > 0.
18-290 Signals and Systems
Spring 2017
Homework 2 Solutions
1. Plot the following equation, x(t), on the interval [0, 2] for the different values of the
parameters , , and specified below:
x(t) = et c
18-290 Signals and Systems
Spring 2017
Midterm 1
1. (10 pts) Suppose that x(t) can be written as
X
x(t) =
ak ejk t ,
k
where ak are scalars. Let x(t) also be periodic with period T . Show that k must
Lab 1 TV Jammer
* Please read and understand the Lab Readiness Prerequisites and
Lab Etiquette and Procedures documents before starting this lab *
1. Introduction
In this lab you will build the core p
18-290 Signals And Systems
Homework 6
Issued: Friday, March 2, 2012
Spring 2012
Total Points: 100
Due: Thursday, March 8, 2012 (in class)
1. Let x(t) and y(t) both be continuous periodic signals havin
18-290 Signals And Systems
Homework 2
Issued: Thursday, January 26, 2012
Spring 2012
Total Points: 100
Due: Thursday, February 2, 2012 (in class)
1. Let z0 be a complex number with polar coordinates (
18-290 Signals And Systems
Homework 4
Issued: Friday, February 10, 2012
Spring 2012
Total Points: 100
Due: Thursday, February 16, 2012 (in class)
1. For the system in the gure, the following is specie
18-290 Signals And Systems
Homework 8
Issued: Friday, March 23, 2012
Spring 2012
Total Points: 100
Due: Thursday, March 29, 2012 (in class)
1. Compute the DTFT of each of the following signals:
(a) x[
18-290 Signals And Systems
Homework 8
Issued: Friday, March 23, 2012
Spring 2012
Total Points: 100
Due: Thursday, March 29, 2012 (in class)
1. Compute the DTFT of each of the following signals:
(a) x[
18-290 Signals And Systems
Spring 2012
Homework 10
Total Points: 100
Issued: Friday, April 13, 2012 Due: Thursday, April 19, 2012 (by noon at the course hub)
1. Let x(t) be a real-valued signal whose
18-290 Signals And Systems
Homework 7
Issued: Friday, March 9, 2012
Spring 2012
Total Points: 100
Due: Thursday, March 22, 2012 (in class)
1. A raised-cosine lter is an LTI system with the following f
18-290 Signals And Systems
Homework 3
Issued: Friday, February 3, 2012
Spring 2012
Total Points: 100
Due: Thursday, February 9, 2012 (in class)
1. Compute the convolution y[n] = x[n] h[n] analytically