This preview shows page 1. Sign up to view the full content.
MATH 2025
Spring 2007
Assignment 3
Due Friday, April 13, 2007
before the class
Please show all work!
1.
Let
f
= 3
ψ
⊗
ϕ
. What is the 2
×
2 matrix corresponding to
f
?
[Here
ϕ
:=
χ
[0
,
1)
and
ψ
:=
χ
[0
,
1
/
2)

χ
[1
/
2
,
1)
]
(4 pts)
2.
Assume that the
Basic TwoDimensional Haar Wavelet Transform
of a
sample
±
s
00
s
01
s
10
s
11
¶
produces the result
±
2 4
8 6
¶
.
(a)
Explain how
a
= 2 relates to the sample.
(5 pts)
(b)
Explain how
h
= 4 relates to the sample.
(5 pts)
(c)
Find
s
00
,s
01
,s
10
,s
11
.
(5 pts)
3.
Calculate the
twodimensional Fast Haar Wavelet Transform
for the data
˜
f
=
3 1 9 7
7 9 5 7
8 6 7 3
2 4 8 6
.
(6 pts)
4.
Let
f
(
x
) =
x
2
.
The
Discrete Fourier Transform
transforms the se
quence of four numbers
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: f (0) ,f ( 1 4 ) ,f ( 1 2 ) ,f ( 3 4 ) into a sequence ( c ,c 1 ,c 2 ,c 3 ) = ( ˆ f , ˆ f 1 , ˆ f 2 , ˆ f 3 ) of four complex numbers. a) Use Fourier matrix 4 F Ω to ﬁnd ˆ f 3 . (5 pts) b) Use the RHS of the equation 4 F Ω = 1 0 1 0 1 i 1 01 0 1i 1 1 0 0 1 i 2 0 0 0 0 1 1 0 0 1 i 2 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 . to ﬁnd the column vector [ ˆ f , ˆ f 1 , ˆ f 2 , ˆ f 3 ] T . (5 pts)...
View
Full
Document
This note was uploaded on 11/23/2011 for the course MATH 2025 taught by Professor Staff during the Spring '08 term at LSU.
 Spring '08
 Staff
 Math

Click to edit the document details