# Is there a difference between correlation processing and matched filter processing?

Is there a difference between correlation processing and matched filter processing? To me, they look same.

• If you don't get much attention (i.e., answers), you may want to ask this on crossvalidated Commented Jul 8, 2014 at 14:37
• I am new to a q&a site. I may follow your suggestion. Now, perhaps I know the purpose of crossvalidated. Commented Jul 8, 2014 at 14:52
• i tried it now at crossvalidated. It says that it does not meet the quality standards. Commented Jul 8, 2014 at 15:25
• This sounds like a telecommunications or signal processing problem. You're thinking of a block diagram processing a signal with various filters to detect a transmitted symbol, correct? Commented Jul 8, 2014 at 17:26
• yes. you are right. Commented Jul 9, 2014 at 0:11

I believe OP is asking about the matched filter of signal processing, and another implementation called a correlation receiver. I believe this is off-topic on this site, but I'll keep you from having to go elsewhere to get your question answered.

Briefly, the correlation receiver does the following:

1. Multiplies the input signal by a basis waveform
2. Integrates that product up to a symbol period $T$
3. Samples the output of the integrator at the time $T$
4. Resets the integrator and starts accumulating again

The sampled output at the time $T$ is the maximum correlation between the input signal and the basis waveform. It's a single number. This design only requires that you can generate the basis waveforms, and have a mixer and integrator per basis.

On the other hand, the matched filter is a filter whose impulse response is a time reversed version of a basis function. There is no mixer, no integrator, and no signal generator for the basis function. The input simply goes through the filter and the correlation function comes out the other end.

They implement the same functionality, but they are clearly different. One is a simple linear filter, the other is a nonlinear operation (mixing) followed by integration. The correlation receiver is much more common in analog, since it is very complicated to design an analog filter whose impulse response is some complicated pulse shape / symbol. Imagine your symbols are 2048 bit long pseudorandom sequences; can you design an analog filter that has a specific pseudorandom sequence as an impulse response? On the other hand, generating that pseudorandom sequence, multiplying it by the input, and integrating in analog are all easily implemented. If you're working in digital however, your DSP chip could implement the matched filter directly. This is why they teach you both topologies for receivers.

• Thank you for your time and clear explanation. Your answer addresses my question completely. But I have the following points. Commented Jul 9, 2014 at 0:01
• Thank you for your time and clear explanation. Your answer addresses my question completely. But I have the following points. "They implement the same functionality" - I agree. You must have been right. A book also says the same thing. But I think I am missing some thing. To me the implementation also appears the same. The filter impulse response is related to the signal. Filtering with a time-reversed impulse response is same as correlation. Filtering also has mixing (multiplication) and integration. Mathematically, to me they are identical. Digital implementation has advantages. Commented Jul 9, 2014 at 0:10
• Just as $\sin(x)$ is calculated using different algorithms depending on what computer, calculator, or package you're using, so too are these two circuits different implementations of the same input/output relationship. Commented Jul 10, 2014 at 0:53
• To say more, the implementation is HOW the thing achieves the desired operation. Both circuits achieve a correlation operation in different ways, i.e., a linear convolution vs. a nonlinear operation followed by an integrate and dump. Filtering looks like it has a mix and integrate, but I promise you that a linear filter circuit of resistors, capacitors, and inductors has no non-linear mixers hiding inside of it! Two real circuits that perform these operations look very different, and are made of entirely different components. They are different implementations of the same mathematical idea. Commented Jul 10, 2014 at 0:54

Basically a correlator is a device that performs correlation of a received signal with its template within a given window of time. In digital communication systems, that window of time is the symbol duration $T_M$. However, the concept of matched filter is also derived starting with the definition of correlation as well (correlation is what anything "matched" to something would do)!

The main difference is that the correlator resets itself at each optimal sampling instant $T_M$ and starts computing the correlation again from zero for the next symbol. This is shown in Figure below.

$\hspace{2cm}$

After the great advancement in computational power, most of the analog circuits capable of performing analog signal processing (e.g., by using resistors, capacitors, insulators, op amps and so on — basically physics and devices) have been replaced by powerful digital processors that can perform the necessary number crunching (basically algorithms run by computer programs) at a much better price vs performance point. Now, design and implementation of matched filters for any kind of applications is much more convenient as compared to the past, requires less bookkeeping and combines efficiently with other receiver blocks such as synchronizers and equalizers.

To conclude, the matched filter computes true correlation of the received signal with the template signal for the duration of the whole symbol sequence, while the correlator resets itself to zero every symbol time.

• Showing the integrate-and-dump circuit resetting to zero really drives this home in a way I could not describe with words alone. Well done. Commented Dec 14, 2021 at 15:04