# Matched Filter Vs Correlator Receiver

Started by April 11, 2006
```Proakis seems to want to differentiate between these two
architectures.  What's the difference?

Whether you integrate the output of f(t)r(t), or input r(t) into a
filter with impulse response f(-t+T), it's all the same. No?
--
%  Randy Yates                  % "Watching all the days go by...
%% Fuquay-Varina, NC            %  Who are you and who am I?"
%%% 919-577-9882                % 'Mission (A World Record)',
%%%% <yates@ieee.org>           % *A New World Record*, ELO
```
```Randy Yates wrote:

> Proakis seems to want to differentiate between these two
> architectures.  What's the difference?
>
> Whether you integrate the output of f(t)r(t), or input r(t) into a
> filter with impulse response f(-t+T), it's all the same. No?

Assuming you mean a data receiver the big difference that I see is that
the filtering solution implies that you're doing the convolution
(correlation) each input sample, while the correlation method does the
correlation (convolution) once for each bit decision.

I see no fundamental mathematical difference, though.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

```
```Tim Wescott <tim@seemywebsite.com> writes:

> Randy Yates wrote:
>
>> Proakis seems to want to differentiate between these two
>> architectures.  What's the difference? Whether you integrate the
>> output of f(t)r(t), or input r(t) into a
>> filter with impulse response f(-t+T), it's all the same. No?
>
> Assuming you mean a data receiver the big difference that I see is
> that the filtering solution implies that you're doing the convolution
> (correlation) each input sample, while the correlation method does the
> correlation (convolution) once for each bit decision.
>
> I see no fundamental mathematical difference, though.

Yes, in both cases only the output at time T (symbol period) is
relevent. In that case, they're identical.

(I posted a little prematurely - I need to do some more reading.)
--
%  Randy Yates                  % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC            %  sliding, it's magic."
%%% 919-577-9882                %
%%%% <yates@ieee.org>           % 'Living' Thing', *A New World Record*, ELO
```
```If only the value at the sampling instant is of
interest, then the matched filter and correlator
give the same result, as has been already noted.
But, intermediate results are quite different as
illustrated in
http://courses.ece.uiuc.edu/ece461/spring01/homework/HW04.pdf

--Dilip Sarwate

```
```Randy Yates schrieb:
> Proakis seems to want to differentiate between these two
> architectures.  What's the difference?

As far as I know the correlation receiver is a generalization of the
matched filter receiver. The basic difference is that in a matched
filter receiver you have one filter for each orthogonal basis function
of the signal, whereas in a correlation receiver you have one filter for
each possible combination of basis functions.
```
```"Andreas Schwarz" <usenet@andreas-s.net> wrote in message
> As far as I know the correlation receiver is a generalization of the
> matched filter receiver. The basic difference is that in a matched
> filter receiver you have one filter for each orthogonal basis function
> of the signal, whereas in a correlation receiver you have one filter for
> each possible combination of basis functions.

I don't think that either of the two statements above is correct.
In particular, one can correlate the received signal with each
basis function and then create any desired weighted combination
of the sampled outputs; different filters for different combinations
of basis functions are not needed.

```