# Finding periodicity within sequence of time hacks

I have a series of time hacks for various events that have occurred. Some of these events occur at regular intervals (+/- some small variance) but I do not know what those intervals are and would like to find out. As a overly simplistic example, let's say I have a series of events that have a relative times of:

1, 2, 5, 7, 8, 10, 11, 15, 16, 18, 20, 24, 25, 30, 32, 35, 39, 40, 41, 42, 45, 48, 50

There are two series that occur; one every 5 seconds and one every 8 seconds.


How can I find these interval periods if I have a subset of data, am starting at an arbitrary start point and can take into account the minor variances that occur when recording time? Is FFT the right way to go or is there something simpler such as just calculating differences and find all the multiples with a given tolerance?

• If you want to get useful answers I suggest you use DSP terminology and not Hackers language. Do you mean that you have two signals where one is a repeated event every 5 seconds and the other every 8 seconds? What are the numbers in the examples? Could you provide an actual sampling in time example (your sequence is a growing value of what - time, power, voltage... – Moti Apr 4 '15 at 14:15
• I'm not a DSP guy so can't speak the language. I just thought this was the appropriate forum for this type of question (finding a signal). Like I said, the numbers were a simplistic example to get the point across. So let me reiterate I said it is a time sequence where each time stamp corresponds to an event that occurred. I don't know the intervals before hand and need to find them out. In the example, yes there are two "signals" (or whatever the DSP term is) that occur every 5 and 8 seconds. I'll post some actual data if you think that will help. – user15304 Apr 4 '15 at 16:37
• And what specifically is "hackers language" to you? – user15304 Apr 4 '15 at 19:17
• What are "time hacks"? What do you mean by events? The FFT assumes a "periodic" signal and is carried on a sequence of samples that are equally spaced. You need to be more detailed in explaining the events and what are you measuring every time. based on your limited description it does not seem that FFT is the proper technique to use, assuming that you are sampling a signal. It will be also beneficial if you will provide some information about the 5 sec and 8 sec "events" – Moti Apr 4 '15 at 19:29
• It was an example. Given a series of time stamps (hacks, value, events, etc), can you find one or more repeating intervals within the sequence. In the EXAMPLE, you can find two series where something occurs every 5 and every 8 seconds. Doesn't matter what the "event" is just the fact that something is happening at that moment and a time value is recorded. From the little I know about FFT, it finds frequencies from time which made me think it was the right approach. But I think the bigger issue is the lack of common understanding between DSP and "hacker" language. – user15304 Apr 4 '15 at 20:54