Use MATLAB to plot the frequency response (both magnitude and phase) of the following
discretetime filters.
A. h[n] = [n] + 2 [n 1] + 3 [n 2] + 4 [n 3] + 3 [n 4] + 2 [n 5] + [n 6]
B. y[n ] + y[n 1] + 0.8 y[n 2] = x[n]
The filter defined by
h[n] = [n] + 2
EE 327 Signals and Systems 1
Test 2
Name _
October 24, 2012
RULES
This is a closed book, closed notes test. You are, however, allowed one piece of paper (front
side only) for notes and definitions, but no sample problems. The top half is the same as from
EE 327 Signals and Systems 1
Test 2
Name _
October 23, 2013
RULES
This is a closed book, closed notes test. You are, however, allowed one piece of paper (front
side only) for notes and definitions, but no sample problems. The top half is the same as from
EE 327 Signals and Systems 1
Test 2
Name _
October 28, 2011
RULES
This is a closed book, closed notes test. You are, however, allowed one piece of paper (front
side only) for notes and definitions, but no sample problems. The top half is the same as from
EE 327 Signals and Systems 1
Test 1
Name _
September 21, 2012
RULES
This is a closed book, closed notes test. You are, however, allowed one half of one piece of
paper (front side only) for notes and definitions, but no sample problems. You must staple you
EE 327 Signals and Systems 1
Test 1
Name _
September 20, 2013
RULES
This is a closed book, closed notes test. You are, however, allowed one half of one piece of
paper (front side only) for notes and definitions, but no sample problems. You must staple you
EE 327 Signals and Systems 1
MATLAB Assignment 1
5 Points
Objective
To become familiar with creating signals in MATLAB and then plotting them.
ContinuousTime Signals
You are to plot three different signals using MATLAB.
x1 (t ) = 2e t 5
x 2 (t ) = sin
EE 327 Signals and Systems 1 Homework 7 7 Points 1. Plot the pole positions of the following firstorder systems. What is the final value of the output to a step input? Sketch the step response. 20 a. H (s ) = (s + 2 ) 0 .5 b. H (s ) = ( s + 0 .5 ) 2. Plo
EE 327 Signals and Systems 1
MATLAB Assignment 2
5 Points
Objective
To perform convolution using MATLAB.
Before Getting Started
This assignment deals primarily with manipulating sound waveforms. As a result, having a pair of
headphones or PC speakers will
Signal
Common Laplace Transforms
Laplace Transform
Signal
(t )
1
cos(bt )u (t )
(t T `)
e sT (T > 0 )
sin (bt )u (t )
u (t )
1
s
t cos(bt )u (t )
tu (t )
1
s2
Laplace Transform
s
2
s + b2
b
2
s + b2
s2 b2
t sin (bt )u (t )
t nu (t )
n!
s
1
s+
e (t )u (t
l . Detrmine ano<prcssion tb followingsignals.Simplifr for youraswer.
x(t)
(a)
.)
Sllt+ r(1) ;,r lv,
P. h. Al
Y,G)
I
cfw_ ' ttl' ult'
l'u(+'z)
'
)
(t x,(t)'* (+")' " s)
xlt/:
t
Xr
f * ^ "[ t ) )
('
r(t'r)+ u k.r)'uf+'z',
u(1' e ).
u ,\ 2"(+'
.?
* ,r
EE 327 Signals and Systems 1 Homework 6 1. Perform block diagram reduction on the following block diagrams. Reduce them to a single block.
X(s) K
+

10 (s + 1)(s + 10)
Y(s)
a.
1 s +1
2
+
1 s + 10
+
s +1 s 1 s
X(s) + +
+
Y(s)
b.
(s + 2)(s + 3)
1
2. Given
EE 327 Signals and Systems 1 Homework 5 1. A system defined by the following differential equation.
& + 2 y + 5 y = x & y Given the following input and initial conditions, find the output of the system by solving the differential equation.
x = sin (3t )
y
EE 327 Signals and Systems 1 Homework 4 1. Use the definition of the Laplace transform to prove that
Lcfw_sin (t ) =
s +2
2
2. Use the definition of the Laplace transform to prove that a. L e  at f (t ) = F (s + a ) dF (s ) b. Lcfw_tf (t ) =  ds
cfw_
3
EE 327 Signals and Systems 1 Homework 3 1. Find the output y[n] of the system h[n] to the input x[n]. Use discretetime convolution. a. x[n] = cfw_ ,2,3 where n = cfw_0,1,2 and 1 h[n] = cfw_ ,2,3 where n = cfw_0,1,2 1 b. x[n] = 10 [n + 1] + 5 [n]  5 [n 
EE 327 Signals and Systems 1 Homework 1 1. Determine an expression for the following signals. Simplify your answer.
x(t) 1 1 1 1 (a) (b) 1 t 2 3 t x(t) 3
2. Sketch the following continuoustime signals. a. x(t ) = u (t + 2 ) + u (t 3) b. x(t ) = 5u ( 2t
EE 327 Signals and Systems 1
Final Exam
Name _
December 11, 2012
RULES
This is a closed book, closed notes test. You are, however, allowed one piece of paper (front and
back) for notes and definitions, but no sample problems. You are also permitted to use
EE 327 Signals and Systems 1
Test 3
Name _
November 20, 2013
RULES
This is a closed book, closed notes test. You are, however, allowed one piece of paper (front
side and half of the back side only) for notes and definitions, but no sample problems. You mu
EE 327 Signals and Systems 1
Test 3
Name _
November 28, 2012
RULES
This is a closed book, closed notes test. You are, however, allowed one piece of paper (front
side and half of the back side only) for notes and definitions, but no sample problems. The fr
BB 327 Signals and Systems 1 Name £2: a a a,
Test 1 September 20, 2013
RULES
This is a closed book, closed notes test. You are, however, allowed one half of one piece of
paper (front side only) for notes and denitions, but no sample problems. You must
Draw the magnitude frequency responses from the polezero plots for the following discretetime systems. Determine which filters are finite impulse response filter (FIR filters) and which are infinite impulse response filters (IIR Filters).
1 0.5 0 0.5 
BB 327 Signals and Systems 1 ,. ._
Test 1 September 19, 20l 4
RULES
This is a closed book, closed notes test. You are, however, allowed one half of one piece of
paper (front side only) for notes and denitions, but no sample problems. You must staple your
Frequency Response of DiscreteTime Systems
EE 327 Signals and Systems 1
David W. Graham 2006
Relationship of PoleZero Plot to Frequency Response
Zeros Roots of the numerator "Pin" the system to a value of zero Poles Roots of the denominator Cause the s
Block Diagrams
David W. Graham
EE 327
Block Diagrams
Symbolic representation of complex
signals
Easier to understand the relationships
between subsystems using block digrams
than by looking at the equations representing
them, or even schematics
Often e
ContinuousTime Signals
David W. Graham EE 327
ContinuousTime Signals
ContinuousTime Signals
Time is a continuous variable The signal itself need not be continuous
We will look at several common continuoustime signals and also operations that may be
MATLAB Tutorial
EE 327 Signals and Systems 1
What is MATLAB?
MATLAB Matrix Laboratory
The premier numbercrunching software
Extremely useful for signal processing
Has many builtin functions useful for learning
signals and systems
MATLAB Functionality
Operations on
ContinuousTime Signals
David W. Graham
EE 327
ContinuousTime Signals
ContinuousTime Signals
Time is a continuous variable
The signal itself need not be continuous
We will look at several common
continuoustime signals and also
operati
StateSpace Modeling
David W. Graham EE 327
StateSpace Modeling
Alternative method of modeling a system than
Differential / difference equations Transfer functions
Uses matrices and vectors to represent the system parameters and variables
2
Motivation