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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Section:
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
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