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EE110B  Signals and Systems
Winter 2015
Lab 6
In this lab, we will explore what is known as first and secondorder infinite impulse response (IIR) filters.
Task 1: Consider the LTI system
y[n] ay[n 1] = (1 a)x[n]
with some real a < 1.
a) Find the transf
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110BSIGNALS AND SYSTEMS
HOMEWORK 1
Please turn in on Friday, January 16th, 2015, at the beginning of the class.
Problem 1: Determine whether or not each of the followi
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110BSIGNALS AND SYSTEMS
HOMEWORK 2
Please turn in on Friday, January 23rd, 2015, at the beginning of the class.
Problem 1: Consider an LTI system with the input x[n] =
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110BSIGNALS AND SYSTEMS
HOMEWORK 3
Please turn in on Friday, January 30th, 2015, at the beginning of the class.
Problem 1: Consider a causal LTI system with the input
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110BSIGNALS AND SYSTEMS
HOMEWORK 4
Please turn in on Friday, February 6th, 2015, at the beginning of the class.
Problem 1:
a) Find the DTFS coefficients ak of the sign
EE 110B Signals and Systems
Introduction to
Discretetime Signals and
Systems
Ertem Tuncel
Discretetime signals
Motivation: We may have access to only
periodic samples x(nT) of a signal x(t).
x(t)
T 2T 3T
T
t
x[n]=x(nT)
1
1
2
3
n
Discretetime signals
EE 110B Signals and Systems
Linear and TimeInvariant (LTI)
Systems
Ertem Tuncel
Why LTI systems?
Linear and timeinvariant systems are
especially easy to analyze and design.
In a lot of cases, they are good enough to do
the "signal processing" job.
Am
EE 110B Signals and Systems
LTI Systems Defined by
Difference Equations
Ertem Tuncel
Difference equations
The input/output relation of an LTI system can
sometimes be expressed as a constantcoefficient difference equation.
Analogous to constantcoefficie
EE110B  Signals and Systems
Winter 2016
Lab 4
In a room with concrete walls (or other similar environment), we often notice acoustic echoes. If you do not
talk very closely to a microphone (on a cell phone for example) in such an environment, the microph
EE 110B  Signals and Systems
Winter 2016
Lab 1
Task 1:
Use MATLAB to plot the following sequences from
patterns:
1) x[n] = cos n
2
5
2) x[n] = cos n
2
3) x[n] = cos(n )
4) x[n] = cos(0.2n )
5) x[n] = 0.9 n cos n
5
6) x[n] = 1.1n cos n
EE 110B  Signals and Systems
Winter 2016
Lab 3
Compute, plot, and discuss the discretetime Fourier transform (DTFT)
X(e j ) =
x[n]e
jn
n =
of each of the following sequences. For each X(e j ) , plot the amplitude spectrum:
X(e j ) versus ,
and the pha
EE 110B  Signals and Systems
Winter 2015
Lab 3
Compute, plot, and discuss the discretetime Fourier transform (DTFT)
X(e j ) =
x[n]e
jn
n =
of each of the following sequences. For each X(e j ) , plot the amplitude spectrum:
X(e j ) versus ,
and the pha
EE 110B  Signals and Systems
Winter 2015
Lab 2
Task 1: Use MATLAB to generate a random sequence
for
and set
for
and
.
(a) Consider a discretetime LTI system with the impulse response
h[n] = 0.9 n u[n]
and the output
.
Compute and plot the output
for n =
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EE110B  Signals and Systems
Winter 2015
Lab 4
In a room with concrete walls (or other similar environment), we often notice acoustic echoes. If you do not
talk very closely to a microphone (on a cell phone for example) in such an environment, the microph
EE110B  Signals and Systems
Winter 2015
Lab 5
The ideal lowpass filter
(
H0 (ej ) =
1 /10 /10
0 otherwise
has a timedomain signal
1
n
h0 [n] = sinc
10
10
(
=
sin( n
)
10
n
1
10
n 6= 0
n=0
which is neither causal nor finite. So for practical purposes, i
EE 110B  Signals and Systems
Winter 2015
Lab 1
Task 1:
Use MATLAB to plot the following sequences from
patterns:
1) x[n] = cos n
2
5
2) x[n] = cos n
2
3) x[n] = cos(n )
4) x[n] = cos(0.2n )
5) x[n] = 0.9 n cos n
5
6) x[n] = 1.1n cos n
EE 110B  Signals and Systems
Winter 2016
Lab 2
Task 1: Use MATLAB to generate a random sequence
for
and set
for
and
. You can use rand or randn for this purpose.
(a) Consider a discretetime LTI system with the impulse response
h[n] = 0.9 n u[n]
and the