Modulation
Modulation
Lesson 13
Sec 1.1.6
1.1.6
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Problem (1)
The signal f(t)=(1+mocos t)cos100t is applied
f(
to a series RLC circuit where L=10 h,
C=10 F, R=10k . Calculate v(t), the
voltage ac
Convolution
Convolution
Lecture #6
2CT.3 8
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Convolution Verify your all your results of these
convolution problems using Matlab and its conv function.
Problem (1)
Assume that a system response is
Signal Analysis
Signal Analysis
Lecture #7
5CT.1-2,4
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Mean Squared Error
Problem (1)
Problem (2)
(2)
It is desired to approximate f(t) = sin (t) in the interval 0<t</2 by the
straight line fs(t)=
Fourier Series for Periodic Functions
Fourier Series for Periodic Functions
Lecture #8
5CT3,4,6,7
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Problem (1)
(1)
Compute the Fourier Series for the periodic functions
a) f(t) = 1 for 0<t<, f(t)
Fourier Transforms
Fourier Transforms
Lecture 9
4CT.1-4
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Calculate the Fourier Transform of the network
function for the following networks:
R1
R
1k
Vin
1k
R
10H
1k
Vout
L
Vin
R2
10H
1k
Vout
Vin
More on FT
More on FT
Lecture 10
4CT.5
3CT.3-5,7,8
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Problem (1)
Show that F(j) of an even function f(t)=f(-t) is real
Sh th
Show that F(j) of an odd function f(t)=-f(-t) is
imaginary
Problem (2)
Discrete Fourier Transform
Discrete Fourier Transform
Lesson 11
5DT
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Homework
Problems 6.2-4
n
) for n = 0,1,2,.N - 1.
N
Hint express the sinusoid in exponential form.
6.2 Find the DFT of the seq
Filters
Filters
Lesson 12
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Homework
Find the response to the (t) for
Bandpass filter with lower frequency f1 and upper frequency f2=2
filter with lower frequency
upper frequency
f1
Band-eliminati
Some Review
of Signals and Systems
Lecture #1
1.1 1.3
BME 333 Biomedical Signals and Systems
- J.Schesser
2
What Is this Course All About ?
To Gain an Appreciation of the Various
Types of Signals and Systems
To Analyze The Various Types of Systems
To L
Sinusoidal Response and Discrete Systems
Sinusoidal Response and Discrete Systems
Lecture #5
3CT.2
BME 333 Biomedical Signals and Systems
- J.Schesser
2
Steady State Sinusoidal Response
Steady State Sinusoidal Response
a y + b y + cy = A cos t
y (t ) = A1
Unit Impulse Function
Unit Impulse Function
Lesson #2
2CT.2,4,
3CT.2
Appendix A
BME 333 Biomedical Signals and Systems
- J.Schesser
17
Complex Numbers
Constants:
s = a + jb
Rectangular Form
Complex
Plane
a is called the Real part of s
b is called the Ima
LTI ODE Continued
LTI ODE Continued
Lecture #4
BME 333 Biomedical Signals and Systems
- J.Schesser
50
Introduction of the Operator
Introduction of the p Operator
d 2 d2
dn
p , p 2 ,., p n n
Define:
dt
dt
dt
d 2 y (t )
dy (t )
dx(t )
+b
+ cy (t ) = e
+ fx(
Sinusoidal Response and Discrete Systems
Sinusoidal Response and Discrete Systems
Lecture #5
3CT.2
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Sinusoidal Steady State
Calculate the Sinusoidal Steady State Response of the
network function
LTI ODE Continued
LTI ODE Continued
Lecture #4
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Homework
2st Order ODEs
1.
Using Matlab, plot the response for following systems. Identity what type
of system each is. Submit your code:
a ) x + 1
Systems
Systems
Lecture #3
1.3
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Linear Systems
Is y(t)=x(t)2 a linear system? Prove your
point
point.
Is y(t)=t2 a linear system? Prove your point.
CT.1.3.1
ODE
Solve and plot the solution to
The Sampling Theorem
Lesson 14
Sec 5.3.3
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Problem (1)
A BL signal with maximum frequency 1000 Hz is sampled at
rate of 1000 samples per second, 2000 samples per second, and
4000 samples per secon
Pulse Code Modulation
Lesson 16
Sec 1.1.6
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Problem (1)
A BL signal with maximum frequency 1000 Hz is sampled at
the Nyquist rate of 2000 samples per second. It is then
quantized to 8 levels. What
Laplace Transforms
Lesson 18
6CT.1-4
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Problems: 3.1a,b,
3.1 a, b The following model for mean aterial pressure following an IV infusion
of sodium nitorprusside (SNP) (developed by Slate and Shepp
Solving Systems using Laplace Transforms
Lesson #19
6CT.5-7
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Problems: 3.3,
A LTI system is described as
s 1.9
H ( s ) 5.263
( s 10)( s 1)
Find the impulse response : h(t )
Draw the Bode plot for
Z Transforms
Lesson 20
6DT
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Problems: 2.16-17,2-19,2-25
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework Answers #1
Problems: 2.16
1
y[n] y[n 1] x[n] u[n]
3
1
z
Y ( z ) z 1Y ( z ) X (
Image Processing
Tomography
162
Homework
1.
A tomograph of the brain needs to be taken using 100
slices. The size of the image to be generated is 12
inches square. The finest detail to be imaged is 0.05
inch using a 3 pixel resolution.
i.
ii.
iii.
iv.
Ca
BME 333 Biomedical Signals
and Systems
BME 333 Biomedical Signals
and Systems - J.Schesser
1
Biomedical Signals and Systems
Biomedical Signals and Systems
Quiz #1
There are 5 questions, you need to complete 4
are questions you need to complete
Questions 3
BME 333 Biomedical Signals
and Systems
BME 314 Biomedical Signals
and Systems - J.Schesser
1
Biomedical Signals and Systems Quiz
#2
Choose 4 out of 5
Problems 3 & 5 are mandatory
BME 314 Biomedical Signals
and Systems - J.Schesser
2
Biomedical Signals a
BME 333 Biomedical Signals
and Systems
BME 333 Biomedical Signals
and Systems - J.Schesser
1
Biomedical Signals and Systems
Quiz #3
Grading:
All questions are rated at 25%
You need to complete 4
Questions 4 is mandatory
Do all 5 for extra credit.
Sh
Some Review
of Signals and Systems
Lecture #1
1.1 1.3
1.3
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
1.
Continuous and Discrete Signals Use Matlab to plot the signals; submit your code
1.
2.
2.
Periodic Signals
1.
2.
3.
3.
Show that tan
Unit Impulse Function
Unit Impulse Function
Lesson #2
2CT.2,4,
3CT.2
Appendix A
BME 333 Biomedical Signals and Systems
- J.Schesser
Homework
Complex numbers
Convert 1+j1 to its magnitude/angle representation (phasor)
Convert 1/(1+j1) to a phasor
Draw ejt
Systems
Systems
Lecture #3
1.3
BME 333 Biomedical Signals and Systems
- J.Schesser
32
Some Basic Properties of Linear Systems
Some Basic Properties of Linear Systems
If a system is Linear, or better yet Linear
system is Linear, or better yet Linear
and T