ECE 251D: Homework #1 Solutions
Problem 2.4.1
(a) The beam pattern for a 21element ULA steered in the T direction is given by
B (, T ) = w(T )H v()
1
=
v(T )H v()
N
d
1 sin[ N
(cos cos T )]
=
N sin[ d
(cos cos T )]
=
when N = 21, d =
1 sin[ 21
2 (cos
13.8,13.9
Received April 1968
15
DeepSea AmbientNoise Statistics*
T. AR.\SI,: \.Xl ELtZAB],Yr[ M. hle.\,E
Iludson l.abnrah*rie. (blumbla ! 'niversily,Dobbs
of
Frrry, .Yea,York 10522
The statistics amhientnoise the ocean
of
in
havebeeninvestigated a sing
Some statistical properties of lake surface reverberation
Marshall
E. Frazer
Applied
Research
Lboratorie [lniversitp Texas Austin,
The
of
at
Austin,
Texas
78712
(Received March 1978)
27
This report describes resultsof an experimental
the
study of the prop
[email protected]
Sat, Jan 31 1:16 PM
to [email protected]
cc Guanwen Yao
Subject: ECE 251A / SIO 207B  MidTerm Project Notes
ECE 251A / SIO 207B Class:
Appended below are a few clarifying notes and additional specifications for the midterm project
su
MidTerm Project
Note: You should treat this project as a takehome exam. Thus, you should neither give nor receive
assistance on completing the project. See the Academic Integrity document on TED
(Misc_Handouts/Overview folder). Select one of the followi
'/ Prec.IEEE— sedpnzevIW
0762.
NlllllM 1:12: NONLINlAR lll.ll‘I{lN(i
N  1
SM) = —j : nf(n)ll"‘
ntl
we obtain SW!) as
‘ N'l " ,
,1 I! Y will
.1" .V {7'0 MA)

. — i
.\_,(ii) = — ’ ".
(ml
The complex cepstruin computed on the basis of (3‘) dif~
fers som
The Application of
Generalized Linearity to
Automatic Gain Control
THOMAS G. STOCKHAM, JR., menace, IEEE
Abstract—The important concept of a linear system has been
generalized to include situations in which signals are combined by
processes other than add
Multipath Propagation
I.
Analytic
Look over the solution to Problem #8.64 in [1].
II.
Numerical
Fix n0 = 4 and use the same vertical axis dynamic range on all FFT plots since the desire is to
compare them. Use (radians/sample) or f (cycles/sample) as the
Single Sideband Generation
A. Implement the block diagram shown below (Figure 11.11a in [1]) and demonstrate the successful
generation of both upper and lower single sideband signals.
B. Let xr(n) be 1024 points in length and consist of three low frequenc
Discrete Random Sequences
I.
Random Numbers
A. Generate 1024point sequences of independent random variables which have the following
probability density functions:
1. Uniform (distributed on [0,1]).
2
2
2. Gaussian (mean = mx = E[x] = 0 and variance = x
Spectral Averaging
The purpose of the following assignment is to investigate the effect of segmenting a time
series on estimation of the power spectrum.
Generate a 1024point time series consisting of a bin centered sinusoid (i.e. fk = (1/N) k
cycles/samp
Transfer Function and Coherence Function Estimation
Implement the following measurement model:
low pass
filter
h(n)
w1(n)
y(n)
+
r(n)
w2(n)
where: wl(n) is a Gaussian random sequence with mean = 0 and var = 1.
1
w2(n) is a Gaussian random sequence with me
Critical Values for the Twosample KolmogorovSmirnov test (2sided)
Table gives critical Dvalues for = 0.05 (upper value) and = 0.01 (lower value) for
various sample sizes. * means you cannot reject H0 regardless of observed D.
n2\n1
1
2
3
3
*
*
*
*
*
*
HW#2 Single Sideband Generation
ECE 251A Digital Signal Processing I
Yue Lu (A53076612)
Jan 19, 2015
1
Single Sideband Generation
Objective
In radio communications, SingleSideBand modulation (SS
ECE 251D: Homework #3
1. 3.7.2
2. 3.10.1, Parts a and c
3. Consider a 32 element ULA with six plane waves impinging on the array. The snapshot vector is
given by
Y[n] =
6
X
sl [n]V(l ) + W[n], n = 1, ., M
l=1
Choose the six angle of arrivals as
45 , 60 ,
ECE251D: Homework #5 Solutions
Problem 4.2.1
Consider an 8element circular array with equal spacing between elements. It could also be viewed
as two 4element rectangular arrays with the rst array oriented along the xy axes and the second
array rotated
ECE251DN: Homework #4 Solutions
Problem 4.1.5
(a) 0 = 0
Beam Pattern: The Kaiser window can be computed by
s
2
2n N 1
N 1
Wkaiser [n] = I0 1
,
n
N
2
2
Where = 6, N = 11.
For a broadside array, the separable weights are given as Wx = Wy =
The separable m
ECE 251A / SIO 207B Digital Signal Processing I
Syllabus (*)
Resources
TED (ted.ucsd.edu)
Syllabus
Lectures Notes posted prior to lecture
Assignments
Misc_Handouts
Video Podcasts (podcast.ucsd.edu)
Class Reserves in S&E Library (class te
IEEE TRANSACTIONS ON AUDIO AND ELECTROACOUSTICS
VOL.
AU20. NO. 2
Digital Inverse Filtering A New Tool for Formant
Trajectory Estimation
JOHN D. MARKEL
Speech Commun. Res. Lab., Inc.
Santa Barbara, Calif. 93101
Abstract
A new algorithm, based upon a digit
Homework Reports Grading / Expectations
Numerical grades are given on a 0100 scale. The interpretation is 90100 is equal to an "A", 8090 is a "B", etc.
My expectations for the homework are the following:
(1) Grading
"A" quality work is doing all things
Statistical Tests on Time Series
A.
Generate the following N = 1024 point time series:
1.
2.
Gaussian white noise with E[x(n)]=0 and var[x(n)] = 1.
" A2 %
"&
#
Add to (A1) a sinusoid % ! = ( such that 10 log (SNR) = 10 log $ 2 ' = 0 dB.
$
16 '
# 2! &
3.
R