<< Chapter < Page Chapter >> Page >
An analysis of matched filters in the frequency domain.

The time domain analysis and implementation of matched filters can be found in Matched Filters .

A frequency domain interpretation of matched filters is very useful

SNR s m h m T 2 N 0 2 h m T 2
For the m -th filter, h m can be expressed as
s m T s m h m T H m f S m f f H m f S m f 2 f T
where the second equality is because s ~ m is the filter output with input S m and filter H m and we can now define H m f H m f 2 f T , then
s m T S m f H m f

The denominator

h m T 2 h m 2
h m h m 0 f H m f 2 H m f H m f
h m h m 0 f H m f 2 f T H m f 2 f T H m f H m f
Therefore,
SNR S m f H m f 2 N 0 2 H m f H m f 2 N 0 S m f S m f
with equality when
H m f S m f
or

Matched filter in the frequency domain

H m f S m f 2 f T

Matched filter

s m t s m f s m f f s m f 2 2 f t f s m f 2 2 f t
where is the inverse Fourier Transform operator.

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Digital communication systems. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10134/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital communication systems' conversation and receive update notifications?

Ask