I have a set of signals consisting of impulses at different instant of time i.e. its not a continuous signal. What I want is a mathematically intuitive way to distinguish between any two such signals?
I understand that the time of occurrence of impulses can be used to differentiate between the impulses. But what I need is like a single number that gives a measure of how different two impulse signals are for instance it could be some property of the signal that would be different for any two signals.
Just an additional info the signals are defined on finite duration. I don't know if that info is needed or redundant.
I don't come from a signal processing background so this question could be wrong. Also if I have tagged it wrongly please modify it.
An example of 2 signals would be:
[0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1]
[0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1]
Answer
You may search for the Morphological Gradient. In addition, if you have some marked data, i.e. you've known the types of these signals, then you can simply train a system using the logistic regression, neural network etc, to differentiate these two types. The advantage of these machine learning methods is that you can encode whatever information that you are interested in the system as an additional feature.
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