BME130 BIOMEDICAL SIGNALS AND SYSTEMS (Required for BME and BMEP) Catalog Data: BME130 Biomedical Signals and Systems (Credit Units: 4) Analysis of analog and digital biomedical signals; Fourier Series expansions; difference and differential equations; co
BME 130 Final Exam
Dec. 12, 2008
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BME 130 Mid-term Exam
Oct. 20, 2008
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1. [Warm-up, 30 pts.] Answer the following true/false questions. If applicable, give a one-line
explanation.
(a) Most physiological systems are linear.
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a single output, but multiple
BME 130 Final Exam
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associativity and commutativity) simplify the system in Fig. 1, i.e. orprem them as
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Lecture 02
Emotional Face Processing
6 October 2014
Jie Zheng
What makes us different
from other animals?
6 October 2014
2
Welcome to ECoG World
What makes us different from other animals?
6 October 2014
3
Welcome to ECoG World
What makes us different fro
10
Laplace Transforms
24 October 2014
Midterm Exam 1
Date: October 29, 2014, Wednesday, 4:00pm to 4:50pm
Closed book, closed note, no calculators, cell phone silenced and
put away
Bring pencils and erasers
Covers Homework Assignments 1 and 2, including MA
05
Impulse
13 October 2014
Outline
Impulse as Input
Unit impulse function
Constructing unit impulse function from steps
Breaking down arbitrary inputs into impulses
Examples
13 October 2014
2
Impulse Response: Motivation
x(t)
xi(t)
x(t) = c0xi(t) +c1xi(t-
08
Discrete-Time LTI,
Impulse Response
20 October 2014
Outline
Discrete-Time LTI systems
Linearity example
Time-invariant example
Total Responses in Difference Equations
Impulse Responses
Discrete-time unit step function
Discrete-time unit impulse functio
06
ImpulseResponse,Convolution
15October2014
Outline
Responsestoimpulses
Impulseresponse
Constructingoutputsfromimpulseresponses
Convolution
15October2014
2
Constructingx(t) with (t)
Area = 1
1
x( t )
x( k )pi (t k )
k 0
pi (t k )
lim
0
k
x( k ) pi ( t k
12
Laplace Transforms
3 November 2014
Poles & Stability
From the previous example,
4
7
1
Y (s) =
+
( s + 2) ( s + 1) ( s + 3)
y(t ) = 7 e t 4 e 2 t e 3t
y(t) exponentially decays to zero, so the system is stable
i.e., Re cfw_ak + s > 0 , where a1 = 2, a2
11
Laplace Transforms
31 October 2014
Properties of Laplace Transform
Linearity
L cfw_c 1 f 1 (t ) + c 2 f 2 (t ) = c 1F1 (s ) + c 2 F2 ( s ) for constants c 1 & c 2
Time shift
L cfw_ f (t T ) = e sT F( s )
Complex translation
L cfw_e at f (t ) = F( s + a
Problem 1
8
9
Problem 2
10
Problem 3
Problem 4
Problem 5
Problem 6
3
4
clear all
close all
%hw8_p3.m
f1 = 10;
f2 = 100;
Npt = 1001;
t = linspace(0,1,Npt);
x = sin(2*pi*f1*t) + 0.2*sin(2*pi*f2*t);
figure(1)
plot(t,x)
hold on
num = 1;
den = [1/(2*pi*20) 1];