EL6113 Midterm
Spring 2010
Name:_
Polytechnic Institute of NYU
ID:_
2.5 Hours
Directions: Answer all questions and show all work. Partial credit will be given where
applicable.
1. (15pts) Consider the system:
where is a constant.
Determine the following c
EL611 3
1) An LTI system is to have the transfer function
H ( z) =
z (2 z 2 + 15 / 2 z + 15 / 4)
( z 3)( z 1 / 2) 2
.
a) Sketch the polezero diagram for H ( z ) .
b) If the system is to implemented by stable recursions, find an equation that can be
used
EL611 3
Homework 5
1) Given an LTI system with real impulse response (i.e. the impulse response h( n) has no
imaginary part), show that
a) Any real input gives rise to a real output. Use the convolution sum to show this.
b) If the response to a complex in
EL611
Laplace Practice
Fall 2008
1. State whether the Laplace transforms of the following functions exist and, where they
do exist, find the Laplace transforms and the regions of convergence.
a)
f (t ) 2 e 3t U (t ) 5 e t U (t )
b)
f (t ) 4 e 2 t U (t ) 5
EL611
LTIDifferential Eq
Fall 2008
1. Find the System functions (transfer functions) of the systems described by the
following differential equations. Also, assuming the systems are causal, state whether
or not they are stable.
a) 2 y (t ) 8 y(t ) 6 y(t
EL611
Laplace
Fall 2008
1. State whether the Laplace transforms of the following functions exist and, where they
do exist, find the Laplace transforms and the regions of convergence.
a)
f (t ) 2 e 3t U (t ) 5 e t U (t )
F ( s)
b)
2
5
3s 13
s 3 s 1 ( s 1
Fourier Series 1. For the following signal: x(t) 2 7 6 4 3 2 1 23 56 8 9 time
a) Find the Fourier series b) Plot the spectra versus frequency, = n 0 . 2. Repeat problem 1 for the following signal: x(t) cos(t)
10
10
time
3. Compute the Fourier serie
EE3064: Feedback Control Lecture Notes (Week 2.2) Block Diagram
An Example
Use differential equations to describe the motion of the system and take Laplace transforms of the signals, we have La sIa (s) + Ra Ia (s) = Va (s)  Ke sm (s) Jm s2 m (s) + bsm (s
EE3064: Feedback Control Lecture Notes (Week 2)
Laplace Transform The Laplace transform of f (t), denoted by Lcfw_f (t) = F (s), is a function of the complex variable s = + j, where
F (s) :=

f (t)est dt.
(1)
If we just consider a signal f (t) defined f
EE3064: Feedback Control Lecture Notes (Week 3) Laplace Transform
F (s) =
0
f (t)est dt
(1)
Impulse Signals The unit impulse signal (t) is zero for all t = 0, and satisfies  (t)dt = 1. The unit impulse signal can be considered as an infinitely high and
Homework 9 Fall 2016
Scanned Textbook Problems:
7.8, 7.35, 7.36
Additional Problems:
1. For each of the low pass filter specifications given below use the posted matlab
program op_filt.m to find a filter that meets the specifications. Assume the maximum
e
EL6113
Formula Sheet for Midterm
Fall 2015
T cfw_1 x1 (n) + 2 x 2 (n) = 1 T cfw_x1 (n) + 2 T cfw_x 2 (n)
Linearity
T cfw_x(n n0 ) = T cfw_x(n)n n n
Time Invariance
0
x ( n) h( n) =
x ( k ) h( n k ) =
k =
h( n)
h( k ) x ( n k )
Convolution
k =
<
BIB
Insurance ID Card & Important Information
Thank you for choosing ISO as your plan manager. Here is your insurance ID card and instructions on using the insurance. Our customer service
representatives are always willing to help with questions and concerns.
EL611
Differential Eq
Fall 2008
1. Find the System functions (transfer functions) of the systems described by the
following differential equations. Also, assuming the systems are causal, state whether
or not they are BIBO stable.
a) 2 y (t ) 8 y(t ) 6 y(t
EL6113
Assignment 3
1. Consider the following 3 sequences:
Find and sketch q[n]. Is
Justify your answer.
2. Consider the cascade of LTI systems with unit sample responses
depicted below:
and
Suppose we are given the following information:
Find the output
EL6113
Assignment 2
1. Determine if the following systems are:
a. Memoryless
b. Causal
c. Invertible
d. Stable
e. Linear
f. Time invariant
i. ! ! = cos ! ! 1
ii. ! ! = ! [!] ! ! ! (! ! )
!
iii. ! ! = ! ! ! [! ]
!
iv.
Sampling
1. A set of samples, f (nT ) , is given below. All samples that are not shown are zero.
f (nT )
1
2
T
T
t
2
Find the unique fuction, f (t ) , whose bandwidth satisfies / T that passes
through all of these samples. Your answer may contain the para
EL6113
Sampling Practice
1. A set of samples, f ( nT ) , is given below. All samples that are not shown are zero.
f ( nT )
1
2
T
T
t
2
Find the unique function, f (t ) , whose bandwidth satisfies / T that passes
through all of these samples. Your answer m
Name:_
ID:_
EL6113 Final Exam Spring 2010
Directions: Answer all questions completely in the blue exam book. Clearly identify your results.
Time: 2 Hours, 30 Minutes
1. (20 pts) Consider the following
EL6113 Signals Systems and Transforms
Syllabus
Instructor:
Prof. [email protected] S. Campisi, email:[email protected], LC108
Class TAs:
TBA
Class Time: Friday 1:00PM to 3:40PM
Class Room: JAB474
Text:
Signals & Syst
EL6113
Assignment 3
1. Consider the following 3 sequences:
Find and sketch q[n]. Is
Justify your answer.
2. Consider the cascade of LTI systems with unit sample responses and depicted
below:
Suppose we are given the following information:
Find the output
EL630
Solutions to Sample Final Exam
1. Box 1 contains 3 white, 2 red and 5 black balls. Box 2 contains 4 white, 4 red and 2
black balls. At random, we pick up one ball from each box. Find the probability that these
two balls are in different color.
Solut
1)
The output is given by the convolution sum
h( k ) x ( n k ) .
a) y (n)
k
If h(n) and x(n) are both real then it is obvious that y(n) will also be real.
b) Note that, since h(n) is real we can take the conjugate of the convolution sum equation
above
EL611 3
Homework 6
1) A discretetime causal LTI system has the system function
1 + 0.2! ! (1 9! ! )
! =
(1 + 0.81! ! )
a) Is the system stable?
b) Find expressions for a minimumphase system ! (!) and an allpass system !" (!) such
that
! ! = ! ! !" (!)
Z Transform Solutions
EL611
Fall 2008
1.)
H ( z)
z (2 z 2 15 / 2 z 15 / 4)
( z 3)( z 1 / 2) 2
.
a) H ( z ) has zeros at z 0 , z 4.197 and z 0.447 . It has a pole at z 3 and a
double pole at z 1 / 2 .
b) The ROC for stability must be 1 / 2 z 3 . We then e