Connexions module: m12054 1
Circular Convolution and
Zeropadding
∗
Richard Baraniuk
This work is produced by The Connexions Project and licensed under the
Creative Commons Attribution License
†
Abstract
Introduction to circular convolution with zeropadding.
Circular convolution has a "wraparound eect." Given Figure 1(a) we desire to smooth circular convolu-
tion with
h
(Figure 1(b)) then we get Figure 1(c).
(a)
(b)
(c)
Figure 1:
(a) The horizontal axis is the number of cell phones purchased per month. (c) The plot is
clearly smoother! The wraparound eect can be clearly seen near 1900.
1
Idea
To eliminate wraparound, zeropad
x
and
h
with zeros and then do the circular convolution (Figure 2).
Figure 2
note:
How much to zeropad to guarantee to wraparound?
∗
Version 1.3: Jan 18, 2005 2:14 pm US/Central
†
http://creativecommons.org/licenses/by/1.0
http://cnx.org/content/m12054/1.3/
