This preview shows page 1. Sign up to view the full content.
Homework #1.
1.
Prove the following Fourier Transform relations:
a)
F
{1} =
δ
(
ν
x
)
δ
(
ν
y
)
b)
11
{sgn(x)sgn(y)} =
xy
jj
π
νπ
ν
F
c)
{f(x,y)} =
{f(x,y)} = f(x,y)
±1
±1
FF
F F
d)
F
{f(x,y)h(x,y)} =
F
{f(x,y)}*
F
{h(x,y)}
e)
22
2
2
{
f(x,y)} =  4
(
+
)
F
{
f(x,y)}
πν ν
∇
F²
F
where
2
x
y
∂∂
∇=
+
is Laplasian operator
2.
Suppose that a sinusoidal input
f(x,y) = cos[2 (
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 04/02/2011 for the course ECE 264 taught by Professor Song during the Spring '11 term at UCSB.
 Spring '11
 Song

Click to edit the document details