EEE 304
HW 3
SOLUTIONS
Problem 1:
Do Problems 7.30, 7.31, 7.41 from the textbook.
7.30
The impulse response is the inverse Laplace of the transfer function:
1
1
x (s) =
s +1
s +1
t
yc (t ) = e u (t )
yc ( s ) =
y ( n) = e nT u ( nT ) = n u ( n), = e T
z
EEE 304, HW3
Problem 1:
Estimate the largest sampling interval Ts to allow perfect reconstruction of the signals (x*y
denotes convolution)
1.
2.
3.
sin3 3
+ sin 2
sin3 3
4
sin3 3
2
sin 3
+ sin 2
sin 2
4. sin2 2
Using the shortcuts, (conservative estimate
EEE 304
HW 5
SOLUTIONS
Problem 1:
For the feedback system shown below, compute the transfer functions u/d, e/r, y/d.
d
r
+
e
C(s)
u
P(s)
+
y

u(s)
CP
=
,
d ( s ) 1 + CP
e( s )
1
=
,
r ( s ) 1 + PC
y ( s)
P
=
d ( s ) 1 + PC
Problem 2: (Low Bandwidth Cont
NAME_SOLUTIONS_
EEE 304
HW 1
Problem 1:
Consider the filter with impulse response h(t ) = e
3 t
u (t 1) .
1. Find the transfer function
2. Find the Laplace transform of the output when x(t )
= sin(t )u (t )
3. Find the output by taking the inverse Laplace
EEE 304
Homework 2
SOLUTIONS
Problem 1:
Consider the following systems:
1. Transfer function H ( s ) =
s 1
(Continuous time, causal)
( s + 2)( s + 1)
2. Transfer function H ( z ) =
0.04113 z 2  0.004329 z  0.04545
(Discrete time, causal)
z 2  1.723 z +
EEE 304 Lab #1
Task #1
Using the tf command, design an analog lowpass filter with cutoff frequency 8kHz. You may choose any order of
the transfer function you like.
a)
Provide the transfer function.
Choosing C=5nf, and step of the filter will be 1, then
EEE 304 Lab 1
Basic Speech Processing using LabVIEW
1. Introduction
This lab introduces some fundamental concepts in National Instruments LabVIEW,
through a simple programming example. LabVIEW stands for Laboratory Virtual Instrument
Engineering Workbench
EEE 304 Lab 3
Sampling, Aliasing and Equalization using LabVIEW
Introduction
This lab introduces some fundamental concepts in sampling theory and reconstruction
through intuitive examples. This lab exercise has three major sections:
Study of aliasing effe
EEE 304 Lab 3
Sampling, Aliasing and Equalization using LabVIEW
Introduction
This lab introduces some fundamental concepts in sampling theory and reconstruction
through intuitive examples. This lab exercise three major sections
Study of aliasing effects w
Name:Zijie Li
Class:EEE304
LAB5
Answer: C(s)P(s)=pi+. Because the target phase angle is 70deg, K+(Tjwo+1)+ (1/(jwo)+
(1/(jwo+1)=110
deg.
From
the
equationC(s)*P(s)=1,
we
can
get
that:
=K*sqrt(T^2*wo^2+1)/wo^2)=K*sqrt(T^2+1)=1
K can be solved from the
Name: Zijie Li
Class and Lab No.: EEE 304 Lab 1
Submission Date: 02/05/2016
1, Provide steps for the following: Create two string controls and change their caption to
Username and Password respectively. Change the display style of the second control to Pa
Name: Zijie Li
Class and Lab No: EEE 304 Lab 3
Submission Date: 03/18/2016
Assignment 1
1. To check the aliasing effects for sine waveform, fix the sampling frequency = 2000Hz and
change the input frequency from minimum to maximum. Observe the aliased and
Name: Zijie Li
Class and Lab No: EEE 304 Lab 2
Submission Date: 02/26/2016
Assignment 1
1. The transfer function provided in Exercise 1 represents a low pass system. How can you
justify this from the results of the continuous system? Is the corresponding
Name: Zijie Li
Class and Lab No: EEE304 Lab4
Submission Date:04/08/2016
Assignment1
1. (Effect of carrier frequency in modulation) First of all, fix the message frequency (20 Hz) and
start changing the carrier frequency from 100Hz to 300Hz. What do you ob
NAME
EEE 304: Quiz 3
Two signals 111 (t) and 332 (t), each with a Fourier transform that is zero for w > wM, are combined
using frequency division multiplexing to generate the output signal y(t).
(i) If the carrier frequency of 931 (t) is wcl > wM, what
NAME
EEE 304: Quiz 4
The open loop transfer function of a system is given by H (s) = $33316. Plot the
straight line approximations of the magnitude and phase plots for this function.
_ IO 3(S+l) . (1+5)
HCS) (s+vo)(s+I00) C'*1$6>0+%a
(+Jw) '
HOOD)
NAME:
EEE 304: Quiz 2
Consider the system with input x[n] and corresponding output y[n]. The zeroinsertion
system inserts one zero after every input sample and the decimation system extracts every
fourth sample of its input. Plot the spectrums of U[n], w
EEE 304, HW4
Problem 1:
Consider the transfer functions
1
1
,
()
=
3 2 4 + 2
3 2 4 + 2
Determine their Tustin and FE equivalents for T = 0.1 (DT and CT respectively).
Comment on the frequency range that the frequency responses are expected to match and ve
Linear Algebra MAT342:
Solution HW 2
September 9, 2013
1
Section 1.2
Ex. 6)
a) (0, 1)
3 5
1 1
b) cfw_ , , , 3 with real
4 8
4 8
c) cfw_0, , with , real
1
4
d) cfw_ , 0, , with real.
3
3
Ex. 9)
a) The linear system cannot be inconsistent since (0, 0, 0)
Linear Algebra MAT342:
Solution HW 3
September 20, 2013
1
Section 1.3
Ex. 17)
We have:
"
1 0
1
#"
a11 a12
0
b
#
=
"
a11
a12
a21 a12 + b
#
Thus, in order to obtain the matrix A, we need to have: a12 + b = a22 . Hence:
b = a22 a12 .
2
Section 1.4
Ex. 1)
a)
EEE 304 Lab Exercise 1: Introduction to MATLAB and SIMULINK
1. Introduction to MATLAB
MATLAB is a highlevel technical computing language and interactive environment for algorithm
development, data visualization, data analysis, and numeric computation. Us
EEE 304: WEEK 3 PRACTICE PROBLEMS
Problem 1:
Estimate the largest sampling interval Ts to allow perfect reconstruction of the signals (x*y
denotes convolution)
sin 2 2t
sin 3t
t2
sin 2t
2.
* sin 3t
t2
sin 3t sin 2t
3.
2t
2t
1.
4.
sin 3t
* sin 2t
t
Problem
EEE 304: WEEK 3 PRACTICE PROBLEMS SOLUTIONS
Problem 1:
Estimate the largest sampling interval Ts to allow perfect reconstruction of the signals (x*y
denotes convolution)
sin 2 2t
sin 3t Using the shortcuts, = 4 + 4 + 6 = 14 < 7
2
t
sin 2t
2.
* sin 3t = mi
EEE 304, HW5
Problem 1:
For the feedback system shown below, compute the transfer functions y/d, x/d. What are the
steadystate values for a constant d and when do they approach 0 asymptotically as t goes to
infinity?
d
r
+
e
C(s)
x
+
P(s)
y
_
()
=
,
+ (
EEE 304 WEEK 4 PRACTICE PROBLEM SOLUTIONS
Problem 1:
Consider the transfer functions
1
4 2 + 2 + 1
Determine their FE and BE equivalents for T = 1. Use MATLAB (if available) to find the
amplitude of the worst case difference between the two. (Its interpre
EEE 304: WEEK 5 PRACTICE PROBLEMS SOLUTIONS
Problem 1:
For the feedback system shown below, compute the transfer functions e/d, x/r. What are the
steadystate values of e/x for a constant d/r, and when do they approach 0 asymptotically as t
goes to infini
EEE 304: WEEK 6 PRACTICE PROBLEMS SOLUTIONS
Problem 1:
A system is to be controlled using integral action to remove constant offsets. The system is described by
the approximate relationship y(t) = 3x(t), where x, y are the input and output respectively. S
NAME $0M) TION
EEE 304: QUIZ 1
The ztransform of a stable system is given 'by
1
' H()>
(i) Sketch the polezero plot. Shade the ROC.
(ii) If h[n] = Ah1[n] + Bh2[n], What are MM] and h2[n]?
(iii) Based on the location of poles and zeroes, can you comment on
EEE 304 Signals and Systems II (Fall 2017)
Homework 1 Solutions
1. Define two continuoustime signals:
h(t) =
X
(t 4n),
n=
f (t) = u(t + 2) u(t 2).
Consider the following block diagram, in which a signal x(t) enters an LTI system with impulse response
h(t
1
3. (20 pts.) Suppose we have the following difference equation:
y[n]  (0.1) y[n  l] = x[n] + 2x[n  l]
a) Find the system function H(z) corresponding to this system.
b) Find the poles and zeros of this system.
c) Find the impulse response of this syst
1
3. (20 pts.) Suppose we have the following dierence equation:
y[n] (0.1) y[n 1] = x[n] + 2x[n 1]
a) Find the system function H(z) corresponding to this system.
b) Find the poles and zeros of this system.
c) Find the impulse response of this system.
2
4.
Name:
EEE 304 Signals and Systems II (Fall 2017)
Midterm Exam 1
September 8, 2017
Transform tables and one page of notes are allowed, plus a calculator.
There are 3 problems, each with 4 parts. Each part is worth 8 points. 4 points free!
Find means to der