Math 4355  Fall 2015
Name:
TEST #1
No notes or calculators allowed. Please, write clearly and justify all your steps, to get proper credit
for your work.
(1)[3 Pts] Let
v:
R,4
:
%
and consider the subspace vo C
span cfw_(1,0,
O,
v given by
t), (2,0,0, 1
Math 4355 Spring 2010
Name:
TEST #2
Please, write clearly and justify all your steps, to get proper credit for your work.
(1)[5 Pts] Let f (x) = cos2 (x) .
(a) Sketch a graph of f over the interval [, ].
(b) Expand the function f (x) = cos2 (x) in a Fouri
M
c?
5c
ttl
=
t U T t o.r.l
XLo, ,3f+)
cf *r9 Cx\
: ,IR
f'?r*, cfw_(xt)
d
f , t" ?trL) Jl. : 1 o 'F
I >< ,F
xr
tnrrl
_c6
e
fo
 +
rlztt
I )l>
6
o
x<o
o3x <l
Lzr rF tlx.z
$ o3x!" I
cfw_ f r tr' t
=l
o!&rvw'li't )
l' I ;
96xt)
hrr\
rF xlz
( 6
bru

Background Material
A computer vision "encyclopedia": CVonline.
http:/homepages.inf.ed.ac.uk/rbf/CVonline/
Linear Algebra Review
and
Matlab Tutorial
Linear Algebra:
Eero Simoncelli A Geometric View of Linear Algebra
http:/www.cns.nyu.edu/~eero/NOTES/geomL
Math 4355 Spring 2015
Name:
TEST #2
This is an openbook test. No notes or calculator allowed. Please, write clearly and justify all your steps to
get proper credit for your work.
(1)[2 Pts] Without computing the Fourier coecients, answer the following qu
Math 4355 Spring 2015
Name:
TEST #3
NOTE: This is an openbook test.
No notes or calculators allowed. Please, write clearly and justify all
your steps to get proper credit for your work.
(1) [6 Pts] Let f (x) = eax , where a > 0.
(a) Compute the Fourie
Math 4355 Spring 2014
Name:
HW #4
(1) [8 Pts] Solve Ex 1,8, p.8384.
(2) [4 Pts] This problem is about numerical approximation of functions
using Fourier series.
Let f (x) = x, for x [, ]. We computed in class its Fourier series,
which is also a sine seri
Math 4355 Spring 2014
Name:
HW #1
Please, write clearly and justify all your steps, to get proper credit for your work.
2
(1)[5
( Pts])Let v1 = (v1 , v2 ) and u1 = (u1 , u2 ) be vectors in C and let
2 i
M=
. Prove that
i 3
( )
v1
u, v = (u1 , u2 ) M
v2
de
Math 4355 Spring 2015
Name:
HW #2
Please, write clearly and justify all your steps, to get proper credit for your work.
(13) Solve problems Ex. 7,9,10, p.35, from the textbook.
(4) (Matlab project) Define a variable with the command x=0:0.001:1;
in Matla
MATLAB CODE EX.3.7
% Define time range
k=1:1:256;
tk=2*pi/256*k;
% define the signal
y = exp(tk.^2)./10).*(sin(2.*tk)+2*cos(4.*tk)+.4*sin(tk).*sin(50.*tk);
yhat=fft(y);
% remove high frequency components
m=15;
for j=m:255m
yhat(j)=0;
end
% compute filte
Math 4355 Spring 2010
Name:
TEST #3
Please, write clearly and justify all your steps, to get proper credit for your work. Open book test
(1)[5 Pts] Let
f (t) =
(
t
0
12 t <
1
2
otherwise .
(a) Compute f, the Fourier transform of f .
(b) Express the real
Math 4355 Spring 2010
Name:
TEST #1
No books or notes allowed. Please, write clearly and justify all your steps, to get proper credit for
your work.
(1)[3 Pts] (i) State the definition of orthogonal complement of an inner
product space V .
(ii) Let V = R3
Q m
(64)
TL:
MV
Slum
42m
0133 (":"I'\ 3 l
he.
C9 9491
P
am V1
.
3
g ms
RT G: u L
wk& on
f6 u
Vad'ms
TEST 4* l
CaHPLEna/T 3" Va [AV (5 I.
5(MV3*LX La Va 3
[Sumw I
id F M \mchrg
VJ: cfw_V6V1 5w; :o Vwevag cfw_.9 (9
3JLWM I V0 is than? V
wk V oruosw k)
Math 4355 Fall 2015
Name:
HW #3
Please, write clearly and justify all your steps, to get proper credit for your work.
(1)[8 Pts] Let V = L2 ([, ]) and consider the subspace V0 V given by
V0 = span cfw_1, cos x, sin x
(i) Find an ON basis for V0 (note that
UNIVERSITY OF HOUSTON
MIDTERM EXAMINATION
. Term: Spring Year: 2009
Student: First Name Last Name
'UII Student ID Number
. COW"Ste, Abbreviatlem... Math 4355. Date of Exam. _ .. _March.ll, 200.9
and Number . I g
Time'Period Start time: 5:30pm
C
Math 4355 Spring 2012
Name:
TEST #2
No books or notes allowed. Please, write clearly and justify all your steps to get proper credit for
your work. Please, use a separate page for each problem.
USEFUL FORMULAS:
Sine series. For f (x), x [0, ],
f (x) =
bk
Math 4355 Spring 2012
Name:
TEST #3
No books or notes allowed. Please, write clearly and justify all your steps to get proper credit
for your work. Please, use a separate page for each problem.
(1) [6 Pts] Let
cfw_
(x) =
1
0
0x1
otherwise;
cfw_
g (x) =
x