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
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 4 SOLUTIONS
Solution:
a) We have
ak =
=
=
=
9
2
1 X
x[n]ej 10 kn
10 n=0
2
2
1 X
ej 10 kn
10 n=0
i
2
2
1 h j 2 k0
e 10 + ej 10 k1 + ej
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 5 SOLUTIONS
Problem 1:
a) Applying our knowledge of the z-transform of right-sided exponentials,
X(z) =
1
1
=
1 (1)z 1
1 + z 1
The onl
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 3 SOLUTIONS
a) Let us find y[n] for n 0 only, as we know that y[n] = 0 for all n < 0.
For the particular solution, try yp [n] = K. K m
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 8 SOLUTION
a) When we sketch the magnitude, it looks like below:
T = 0.1
0.1
0.09
0.08
0.07
|H r (j)|
0.06
0.05
0.04
0.03
0.02
0.01
0
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2014
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 6
Please turn in on Friday, February 27th, 2015, at the beginning of the class.
Problem 1: Determine the inverse z-transform of the fo
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 8
Please turn in on Friday, March 13th, 2015, at the beginning of the class.
Problem 1: Consider the standard block diagram for discre
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 5
Please turn in on Friday, February 20th, 2015, at the beginning of the class.
Problem 1: Determine the z-transform of each of the fo
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 7
Please turn in on Friday, March 6th, 2015, at the beginning of the class.
Problem 1: Consider the signal
xc (t) =
sin(t)
t
2
which i
1
EE110B Homework 3
1) Determine the discrete-time Fourier transform of:
a) 0.4n1 u[n 1]; b) 0.3|n2| ; c) [n 1] + [n + 2]; d) sin( 4 n + /4).
2) Consider a system whose input x[n] and output y[n] are related as
5
1
y[n] y[n 1] + y[n 2] = x[n]
6
6
a) Deter
1
EE110B Note 4
Y. Hua
1) Modulation Theory: Given
y(t) = x(t)c(t)
R
we know that Y (f ) = X(f ) C(f ) = X(f v)C(v)dv. If c(t) is periodic, i.e., c(t) =
R T /2
P
k
k
1
c(t + T ), we have c(t) =
k= ak exp j2 T t with ak = T T /2 c(t) exp j2 T t dt,
P
k
an
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 7 SOLUTION
Problem 1:
a) Define the signal rectA (x) as
(
rectA (x) =
1 A x A
0 otherwise
which is nothing but a rectangular pulse sig
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
WINTER 2015
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 6 SOLUTIONS
Problem 1:
a) x[n] = 0.1n u[n].
b) x[n] = 0.1n u[n 1].
c) Multiplying both the numerator and the denominator by z 2 , and
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
SPRING 2017
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 1
Please turn in on Thursday, April 13th, 2017, at the beginning of the class.
Problem 1: Determine whether or not each of the followi
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 discrete-time LTI system with the impulse response
h[n] = 0.9 n u[n]
and the
EE 110B - Signals and Systems
Winter 2016
Lab 3
Compute, plot, and discuss the discrete-time 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 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
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 constant-coefficie
EE 110B Signals and Systems
Linear and Time-Invariant (LTI)
Systems
Ertem Tuncel
Why LTI systems?
Linear and time-invariant 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
Introduction to
Discrete-time Signals and
Systems
Ertem Tuncel
Discrete-time 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
Discrete-time signals
Anthony Chen
861148845
EE 110B Section 001
Lab 2
Objective: To use MATLAB to generate a random sequence and see what using the convolution
integral does to the output.
(a)
(b)
(c) The two outputs are extremely similar.
(a)
Figure out why Part B does not l
Anthony Chen
861148845
EE 110B Section 001
Lab 1
Objective: The objective of this lab in my eyes was to practice plotting sequences onto Matlab
while interpreting the graphs.
Task 1: Use MATLAB to plot the following sequences from to , discuss and explain
UNIVERSITY OF CALIFORNIA, RIVERSIDE
Department of Electrical Engineering
SPRING 2017
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 2
Please turn in on Thursday, April 20th, 2017, 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
SPRING 2017
EE110B-SIGNALS AND SYSTEMS
HOMEWORK 3
Please turn in on Thursday, April 27th, 2017, at the beginning of the class.
Problem 1: Consider a causal LTI system with the input-
1
EE110B Note 3
Y. Hua
1) Sampling Theorem: Consider a continuous-time signal xc (t) and a sequence of its samples
xd [n], i.e., xd [n] = xc (nT ) where T is the sampling interval. The sampling rate is 1/T .
For xc (t), we have the spectrum
Z
Xc (f ) =
xc
1
EE110B Note 2
Y. Hua
1) Fourier Transforms
a) Continuous-Time Fourier Transform (CTFT): for any signal x(t) satisfying
R
|x(t)|dt <
, we can write
Z
x(t) exp(j2f t)dt
XCT F T (f ) =
Z
XCT F T (f ) exp(j2f t)df
x(t) =
b) Continuous-Time Fourier Series (
1
EE110B Homework 5
1) Let xc (t) be a continuous-time signal whose Fourier transform has the property that
n
) is obtained. For
Xc (f ) = 0 for |f | 1000. A discrete-time signal xd [n] = xc ( 2000
each of the following constraints on the Fourier transfor
EE110B - Signals and Systems
Winter 2015
Lab 5
The ideal low-pass filter
(
H0 (ej ) =
1 /10 /10
0 otherwise
has a time-domain 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
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
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