18-290 Signals & Systems
Spring 2013
Homework #1
Total Points: 100
Due: Thursday, Jan. 24, 2013
1. (20 pts) Odd and even functions.
For the following functions, determine if each one is odd, even, or neither. If neither, decompose it into odd and even par
18-290 Signals & Systems
Spring 2013
Homework #10
Total Points: 100
Due: Monday, April 22, 2013
1. (15 pts)
According to the sampling theorem, the frequency that must be exceeded by the sampling
frequency is called the Nyquist rate. Determine the Nyquist
18-290 Signals & Systems
Spring 2013
Homework #9
Total Points: 100
Due: Thursday, March 28, 2013
1. (25 pts)
Compute the Fourier transform of these DT signals:
(a) (5 pts) x[n] = n, f or 2 n 2; x[n] = 0, otherwise
(b) (5 pts) x[n] = u[n + 1] u[n 3]
(c) (5
18-290 Signals & Systems
Spring 2013
Homework #8
Total Points: 100
Due: Thursday, March 21, 2013
1. (15 pts) Fourier transform of an impulse train.
Justify your answers by showing your work or reasoning.
(t kT ), an impulse train with period T , nd the F
18-290 Signals & Systems
Spring 2013
Homework #7
Total Points: 100
Due: Thursday, March 7, 2013
1. (30 pts) Fourier Transforms Of CT Signals
Please justify all your work.
F
(a) (5 pts) If X cfw_j = ( d ), nd the inverse Fourier transform x(t) X cfw_j .
F
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18-290: Signals and Systems
CMU/ECE, Spring 2013
Homework #6 Exam 1
Due: Thursday, February 28, 2013
Show your work! Justify your answers!
Answers that are simply stated without any
j
18-290 Signals & Systems
Spring 2013
Homework #5
Total Points: 100
Due: Thursday, Feb. 21, 2013
1. (20 pts) Fourier series repesentations of odd and even signals.
Suppose that the following information is given:
x(t) is real.
The Fourier coecient a0 = 2.
18-290 Signals & Systems
Spring 2013
Homework #4
Total Points: 100
Due: Thursday, Feb. 14, 2013
1. (35 pts) Evaluating convolutions, causality and stability for CT and DT LTI systems.
(a) (7 pts) Consider the following CT convolution example:
Let the syst
18-290 Signals & Systems
Spring 2013
Homework #3
Total Points: 100
Due: Thursday, Feb. 7, 2013
1. (20 pts) Memory, causality and invertibility in systems.
For the following systems, determine if they are memoryless, causal, and invertible. If no,
explain
18-290 Signals & Systems
Spring 2013
Homework #2
Total Points: 100
Due: Thursday, Jan. 31, 2013
1. (20 pts) Periodicity after time scaling, time shift, and summation.
Let x(t) be a continuous time signal, and let y1 (t) = x(3t) and y2 (t) = x(t/3). For ea