ECE633 Signals and Systems I, Fall 2009 Homework 1 Solutions From: Linear Systems and Signals, 2nd ed. B. P. Lathi, Oxford University Press, 2005. B.1 Given a complex number w = x + jy , the complex conjugate of w is defined in rectangular coordinates as
Recitation 3: ZIR
Eileen Hwuang
ehwuang@seas.upenn.edu
9/16/2016
Office hours: Next Wednesday, 9/21 from 5-6pm in Hayden Lobby
Deriving System Response
Differential system structure
Q(D) and P(D) are differential operators
system
input
output
In zero inpu
BE301, Exam #1, 10/2/14, Part B [22 points) Name (1 point)
Problem 1: Prove or explain. Yes/No answers are not acceptable. YOU can refer to basic
properties of functions or operators, but need to be specific. (if the answer is negative you can
give one ex
BE301, Fall 2016
Bioengineering Signals & Systems
Classification of Systems
Part 2, Systems
Developing Systems Concepts and Tools
Input
x(t)
Output
y(t)
System
Classification of systems
Linear and nonlinear
Time invariant (constant parameters) and time
BE301
Example to show that the derivative operator is not a stable system in the Bounded Input Bounded
Output Sense (BIBO). We will prove that by taking the derivative of the step function
which is clearly bounded, results in the delta function
which is u
A general 2nd order Example.
Real system with real nonnegative ODE coefficients
() + () + () = ()
The characteristic polynomial is: + +
The characteristic equation is: + + =
The characteristic roots are: =
+
,
Initial conditions are: ( = ) = , ( = ) =
BE301, Part 4
Bioengineering Signals & Systems
Zero State Response
Convolution
Fall, 2016
Zero State Response
For linear time invariant systems
Total response =
zero-input response + zero-state response =
ZIR+ ZSR
Zero State Response
We will investigate
BE301, Fall 2016
Bioengineering Signals & Systems
Part 3, Linear Differential Systems
System Equivalence
Zero Input Response (ZIR)
Systems, where do we go from here?
http:/biomed.brown.edu/
Types of systems we will study
Linear time invariant systems
In
BE 324
Problem Set 8
December 1, 2016
1. During PCR, double chains of DNA are dissociated by heating. It is known that at 310
K, double stranded DNA is only 3 % dissociated. Calculate
(a) the equilibrium constant at 310 K.
(b) G*
(c) Given that * = 150 kJ
BE 324
Problem Set 7 Solutions
1. Physiological saline is water with NaCl dissolved at a concentration of 0.15 M.
a) What is the boiling point of physiological saline?
b) What is the osmotic pressure of physiological saline?
Note: 310K is used here for te
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BE 324
Final
DecemberplS, 2015
Name
Open book, open notes
53 was
My signature below indicates I have complied with the University of Pennsylvanias code of
academic integrity in completing this examination:
Name (printed)
Name (signed)
If needed, use the B
Name 35 J 3" N5
BE 324
Final Examination
December 18, 2013
Open book, open notes
My signature below indicates I have complied with the University of Pennsylvanias code of academic
integrity in completing this examination:
Name (printed)
Name (signed) Date
BB 324
Problem Set 9
Thursday, December 8, 2016 in class
1. Dill and Bromberg, Chapter 17, Problem 2.
a) in-lemle 'leC. e
" ~11 :
656:1: 5-7CCK\ 3%Xz+b><+d
b) 1.
: ~D (1:03'12 . z -
7(03 W .7: (2(0\ M R71: (
3 (k\= %(2(m-lb : 22:
WM
0
m m" mm +1310 3913
Name sob
BB 324
Midterm 1
October 6, 2015
Open book, open notes
My signature below indicates I have complied with the University of Pennsylvania's code of
academic integrity in completing this examination:
Name (printed)
Name (signed) Date
If needed, use
BE301
Fall 2016
1
Is this system
A Linear?
2
y (t)=2 x (t)
3
4
y (t)=2 x 2 (t1)
y (t)=2 x (t +1)
5
y (t)=cos(x (t )
y (t )=2 t [ x ( t1 ) ]
Yes.
Consider:
Yes.
Consider:
No.
Consider:
Yes.
Consider:
No.
Consider:
Yes.
Yes.
System does not have
Yes.
No.
Sy
LinearSystems,Example
Showthatthesystemdescribedbytheequationislinear.
Let x1(t)
Letx
(t) y1(t)
(t) andx
and x2(t)
(t) y2(t),then
(t) then
and
Multiply1st equationbyk1,and2nd equationbyk2,andaddingthemyields:
This equation is the system equation with
This
BE301, Fall 2015, HW4
Page 1
Part A
BE301, Fall 2015, HW4
Page 2
2.4-18 d,f
2.6-5. (a) For < 2 and 4, note that = 0
For 2 < 0: =
!
!
For 0 < 2: =
!
!
For 2 < 4: =
!
!
=
!
ECE633 Signals and Systems I, Fall 2009 Homework 3 Solutions From: Linear Systems and Signals, 2nd ed. B. P. Lathi, Oxford University Press, 2005. 1.6-1 Write the input-output relationship for an ideal integrator. Determine the zero-input and zero-state c
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ECE633 Signals and Systems I, Fall 2009 Homework 8 Solu