# Measure resonant frequencies from system output data

1. Suppose I have a real (physical) dynamical system with one capacitive sensor, and I also have the ability to extract data for this system in csv form. The system data output is shown below (graphs) for various sampling frequencies.

2. As the system is real time and its output depends on the immediate environment (temperature, pressure, etc..) I need to be able to determine if the sampling frequency is hitting any harmonics on-the-fly. All I have is data.

How, in general, can I determine resonant frequencies from data?

• "I need to be able to determine if the sampling frequency is hitting any harmonics" - are you saying that you want to determine if the sampling frequency is subject to aliasing, whereby the output signal is not representative of the inputs because occasional peaks (from resonant effects) are being hit? Generally speaking you cannot detect resonance without also sampling your inputs otherwise you don't know if the output is a result of one input or the interaction of multiple inputs. – PAK-9 Mar 27 '19 at 22:45
• Thanks for your comment PAK-9. In this case, the Output (Capacitance) is a linear function of a Single Input (Time in uS). I could sample the Input as you suggest, but this would give me the same charts (albeit on different scales). I know, from looking at it, when a time series features resonance. But my routine doesn't. Hence my question: How can I, from sampling data continuously, determine that resonance is taking place, thus giving me the opportunity to jitter the sample frequency or hop on a different one to avoid resonance? – Jeruinsky Mar 28 '19 at 15:17
• I am looking for a statistic I could calculate on the fly to evaluate the proposition... if this makes sense. – Jeruinsky Mar 28 '19 at 15:17
• "I know, from looking at it, when a time series features resonance." - how? What feature are you using to decide that resonance is occuring? If it is something as simple as amplitude > x then you need to implement a peak detection algorithm which matches that. I'm not 100% following your methodology but in principle the sample frequency is not something you should be considering, just use the highest sample rate you can and focus your attention on signal processing of the final data. – PAK-9 Mar 29 '19 at 17:00
• I see what you are saying. For example, look at the middle chart above. I only get this behavior from sampling at 3350uS/cycle. This feels like resonance to me, yet, the amplitude of the signal is very similar to the two previous ones. – Jeruinsky Mar 30 '19 at 12:27