How to campare signals with different length?

Hi

Can someone help me out please? If I have a set of signals with different length. How can I compare them with the reference one and get the similarity or kind of correlation.

For example I have a reference signal with 75 samples. 10 signals with different length between 65 to 80. I would like to use those 10 signals to compare with the reference one by one and see how similar they are.

I know the correlation if I have the signals with the same length but I am confusing about how to do it with the different length signals. I have a roughly idea is make those 10 signals shifting from left to right of reference signal but I dont know which output should I do to compare the similarity.

Thanks for your help!

Best Regards

Answer 1

[Star Strider]

One option may be the Signal Processing Toolbox findsignal function (introduced in R2016b). The signal lengths are not important.

The function also produces a third output that is the Euclidean distance between the two signals, so that will be a measure of their similarity.

[BoWen Han]

Hi Thanks for your help. Sorry for reply late. That is really helpful and ispire. Can I ask a stuip question is how the Euclidean distance present similarity? If I got the result around 300 can I say it is similar or kind of repeat one?

Thank you

[Star Strider]

My pleasure!

No worries!

The distance (that does not necessarily need to be Euclidean — see the Metric documentation section for those that are offered) is a measure of similarity. I am not certain how to convert it to a statistical measure (for example with confidence limits or probabilities) although it might be possible to use the mean of that section of the signal as a reference, calculate that distance using the same metric (this would have to be done manually) and then compare the ratio of the two distances. I am not certain how best to present this however, since the ratio would be between two scalars, so it is not immediately obvious to me what statistical test could be used. (The F statistic — using the fcdf function — seems likely, however it would be best to discuss this with a statistician to be certain it is calculated correctly and and presented correctly. I never thought about this previously in this context.)

So the only relatively simple approach I can provide is to compare the distance calculated by findsignal with the distance from the mean of the signal in the same region, calculated the same way using the same metric. I am not certain what statistical measure would be best, althoug there should be one that would be appropriate.

.

[BoWen Han]

Thanks for your help! I will look into it. Thanks for all your suggest xd

[Star Strider]

As always, my pleasure!

Answer 2

[Jan]

It depends.

You can compare two sine waves, if one has 80 and the other one 75 samples. But how do you define "similarity"? You can shift the phase, interpolate to change the frequency, shift the signal up and down and amplify the values until the curves are matching. But are they more similar, if you have to adjust only the phase or only the amplitude?

How similar are two sin waves, if the second one equals the first one plus some noise?

Before you can implement this in Matlab, you have to define mathematically (or even better physically), what you want to compare. Otherwise the results are arbitrary:

What is the difference between a blackbird? - Both legs have the same length, especially the right one.

[BoWen Han]

Thanks for your help and sorry for late reply. Yeah this is the point I am struggling how to define the 'similarity'. I have some results now but it is hard to say how the result can present similarity.

Thank you