This preview shows pages 1–7. Sign up to view the full content.
Convolution and Filtering: The Convolution Theorem
Convolution and Filtering:
The Convolution Theorem
CS 450: Introduction to Digital Signal and Image Processing
Bryan Morse
BYU Computer Science
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Convolution and Filtering: The Convolution Theorem
Introduction
Linear Systems and Responses
Time/Spatial
Frequency
Input
f
F
Output
g
G
Impulse Response
h
Transfer Function
H
Relationship
g
=
f
*
h
G
=
FH
Is there a relationship?
Convolution and Filtering: The Convolution Theorem
Convolution Theorem
The Convolution Theorem
Let
F
,
G
, and
H
denote the Fourier Transforms of signals
f
,
g
,
and
h
respectively.
g
=
f
*
h
g
=
fh
implies
implies
G
=
FH
G
=
F
*
H
Convolution in one domain is multiplication in the other
and vice versa.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Convolution and Filtering: The Convolution Theorem
Convolution Theorem
The Convolution Theorem
Thus,
F
(
f
(
t
)
*
g
(
t
)) =
F
(
f
(
t
))
F
(
g
(
t
))
Likewise,
F
(
f
(
t
)
g
(
t
)) =
F
(
f
(
t
))
* F
(
g
(
t
))
Convolution and Filtering: The Convolution Theorem
Convolution Theorem
Filtering: FrequencyDomain vs. Spatial (Convolution)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Convolution Theorem
Linear Systems and Responses
Time/Spatial
Frequency
Input
f
F
Output
g
G
Impulse Response
h
Transfer Function
H
Relationship
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 03/02/2012 for the course C S 450 taught by Professor Morse,b during the Winter '08 term at BYU.
 Winter '08
 Morse,B

Click to edit the document details