580.222 - BIOMEDICAL SIGNALS AND SYSTEMS
Spring 2007 - Practice Exam 2 / Homework 5 Solutions
Distributed: Wednesday, Feb. 28, 2007
Due: Monday, March 5th, 2007
Problem: 10
For the continuous time signal
x(t) = 2 + j cos(2t) + e
jt
3
.
Calculate T and plo
BME 221 - BIOMEDICAL SIGNALS AND SYSTEMS
PROBLEMS
Problem
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Problem
1:
2:
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7:
10
20
10
10
15
15
15
points
points
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NAME:
SECTION:
Section
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Section
1:
2
2+2a
2+a +a 2
2+a +a 2
a
-5
-4
-3
-n
(1+a +a 2 )
-2
-1
a n-2 (1+a +a 2 )
0
1
2
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4
5
4. (2.41 from O and W). consider the signal x[n]=nu[n].
(a)sketch the signal g[n]=x[n]- x[n-1].
g[n]= nu[n]- n-1u[n-1]= n (u[n]- u[n-1])= n[n]= [n]
(b)use the result of
After your sophomore year in BME at Johns Hopkins, you get a prestigious internship from
Medtronics. You are tasked with working on the improvement of an electrocardiograph machine
by analyzing system responses. You are to analyze the effects of noise [n]
Problem3 (10 points)
The multiplication property of Fourier transform. Let X(jw) be the Fourier transform of x(t), H(jw)
be the Fourier transform of h(t), Y(jw) be the Fourier transform of y(t), if
Y ( jw)
if Y ( f )
1
( X ( jw) * H ( jw) , prove that y(t
Problem 2 (10 points)
A periodic signal x t (saw-tooth wave) with fundamental period T = 4 is defined
over ONE period as:
x t
t,
2 t
2.
The Fourier series coefficients of
are represented by X k .
a) (5 points) Determine the value of X 0 . Show your work.
BME 222 - BIOMEDICAL SIGNALS, SYSTEMS and CONTROL
Exam 1- 12-1:15 Wednesday February 27, 2013
Exam 2 - 12-1:15 Wednesday March 13, 2013
SPRING 2013 - HOMEWORK SET 3
Distributed: Wednesday February 13, 2013
Practice: Last years test, Monday in class Februa
BME 222 - BIOMEDICAL SIGNALS, SYSTEMS and CONTROL 2013
Exam 1- 12-1:15 Wednesday February 27, 2013
SPRING 2013 - HOMEWORK SET 2
Distributed: Wednesday February 6, 2013
Due: Wednesday February 13, 2013
READING ASSIGNMENT
Oppenheim, Willsky, with Nawab, Ch.
BME 222 - BIOMEDICAL SIGNALS, SYSTEMS and CONTROL
SPRING 2013 - HOMEWORK SET 6
Distributed: Friday March 8, 2013
Due:Wednesday March 13, 2013 (day of Exam 2) before noon in Clark 318
READING ASSIGNMENT
Oppenheim, Willsky, with Nawab, Ch. 1,2, Ch. 4, secti
Chapter 2 - Solutions to Exercises
Systems and Controls (BME 580.222)
Instructor: Sri Sarma, Email: sree@jhu.edu
April 16, 2013
1. (30 points) Let us (t) be the unit step function. Find the Laplace transform and region of convergence of the
following time
BME 222 - BIOMEDICAL SIGNALS, SYSTEMS and CONTROL
SPRING 2013 - HOMEWORK SET 5
Distributed: Monday March 4, 2013
Due:Friday March 8, 2013 in section
READING ASSIGNMENT
Oppenheim, Willsky, with Nawab, Ch. 1,2, Ch. 4, sections 4.1-4.3 pages
284-306.
PROBLEM
BME 222 - BIOMEDICAL SIGNALS, SYSTEMS and CONTROL
Exam 1- 12-1:15 Wednesday February 27, 2013
Exam 2 - 12-1:15 Wednesday March 13, 2013
SPRING 2013 - HOMEWORK SET 4
Distributed: Wednesday February 20, 2013
Due: Textbook Problems due Wednesday February 27,
Chapter 5 - Solutions to Exercises
Systems and Controls (BME 580.222)
April 19, 2013
1. (15 points) Imagine that as you are reading this question, you decide to reach for a pencil. You lift your
eyes from the paper and try to locate the target. The usual
Chapter 3 - Solutions to Exercises
Systems and Controls (BME 580.222)
Instructor: Sri Sarma, Email: sree@jhu.edu
April 23, 2013
1. (25 points) Consider the linear system with the following state-space representation.
0 1
0
0
1 x(t) + 0 u(t), x(0) = 0,
x
Chapter 4 - Solutions to Exercises
Systems and Controls (BME 580.222)
April 19, 2013
1. (30 Points) Transient Behavior Revisited
Consider the following open loop transfer function for a second order system with an added zero:
G(s) =
2
n s + n
.
2
s2 + 2n
Chapter 3 - Solutions to Exercises
Systems and Controls (BME 580.222)
Instructor: Sri Sarma, Email: sree@jhu.edu
April 12, 2013
1. (25 points) Consider the linear system with the following state-space representation.
0 1
0
0
1 x(t) + 0 u(t), x(0) = 0,
x