# Detecting expected patterns in repeated measurements

I am new to signal processing and I am trying to learn myself. To understand what i am interested in, let me show this on example (note that this is just a random example to illustrate). Here is some signal detected from a device:

You can notice there are 3 peaks there, and let's say there is a task to detect times of beginning of each peak (where it starts to rise). I then need to evaluate times of these 3 peaks and compare it to expected value. Now I am interested in ways how to detect these "patterns" and I am trying to find more info/learn about (something general, not specifically to this signal).

So far I learnt how to use basic filters to get rid of noise (moving average, exponential smoothing) and some really simple techniques how to find some of these points (checking sudden changes (difference between two successive filtered values) in the filtered value that is above certain threshold, etc...). My question is, where can I get to know more about this area, if you can point me to some resources, direction... Something that is not about finding unknown patterns in signal, but more about being able to accurately detect already known/expected "patterns". I will be thankful for any info/references.

So far I learnt how to use basic filters to get rid of noise (moving average, exponential smoothing)

Those are all low-pass filters!

checking sudden changes (difference between two successive filtered values)

That is a high pass filter !

To be honest, I don't see "patterns" in your signal, the peaks are all pretty different, but you don't care for "patterns", either:

You really are just interested in the signal that first passes through a low-pass filter, and then a high-pass filter.

Combined, that is a band-pass filter.

So if I'd recommend something: Look into filtering; understand the spectrum of signals, and understand how to build filters that extract specific signals from the original signal.

• Have you heard about Wiener filters? en.wikipedia.org/wiki/Wiener_filter Aug 16 '16 at 17:42
• @rrogers yes, but wouldn't you need to know at least the PSD of the stationary process you're looking for? Aug 16 '16 at 17:50
• "more about being able to accurately detect already known/expected "patterns". ? Therefore you can estimate the PSD? Aug 16 '16 at 18:35
• @Sil Not knowing the physical source; I would do a normal/quantile probability plot and examine the out of bounds changes. There are a lot of possibilities but one is to assume that the jumps are due to impulse hits. How about a clue:) What is the signal and interference physically? Aug 16 '16 at 18:45
• The actual source is sensor of air pressure during opening/closing of the valve. The image here is just illustratory, but yes the signal on every opening/closing cycle is similar always, I guess that could be used. But the thing is that it can be stretched in time axis (some of the events can occur sooner/later, that is basically what I am trying to figure out, if these are not happening too late, lets say sudden increase in pressure should always happen within 0.5 second form the beginning, etc..). Anyways I am going to read something about what you guys referenced, seems interesting.
– user23308
Aug 17 '16 at 10:14