# Correlation between a lowfrequent and a fast signal

I need to evaluate the correlation between some measured signals. Those signals are for example current, temperatures at various points, vehicle speed and torque from an electric motor in a vehicle. I have them as timeseries-objects. Now what I want is to know which signals are the most correlated ones with my temperaturesignal of the motor. (for later to make a temperature-model, to see which I should include in the model) I already tried to use pearsons correlation coefficient which worked for some signals, but not for the correlation between the temperature and the power loss, which should be correlated by physical nature.

corrcoef -> correlation of 0.029 in first data set

In this image you can see the power loss and the temperature. Everytime the loss is high, the temperature rises slightly, but how can I measure this dependence? What would be a good way to get the correlation between a low-frequent temperature signal and a fast one like voltage and current? Do I need to modify my signal with a lowpass filter?

I also tried xcorr without shifting, but then the speed of the vehicle is more correlated than my power loss, that doesnt seem like the right way either.

• This is just a hint: since the power loss is related to the temperature growing rate, the correlation should be looked for between the data about the power loss inside the motor and some numerical approximation of the derivative of the temperature time trend. – Vexx23 Oct 28 '16 at 14:48
• If I was doing this I would start by doing several things: 1) Construct various (all?) a vs. b (vs. c) graphs and look for likely patterns. 2) have you actually looked at the timewise cross-correlation graphs? 3) If your statistically competent try "factor analysis". 4) make up what you think is a "signal flow" diagram and then fabricate tests that validate (or invalidate) your diagram. Are you operating under the presumption that temperature is a cause (or effect) of power loss. I could make arguments on either side. Not much more help here. – rrogers Nov 1 '16 at 17:57
• Thank you for the help. @rrogers What do you mean exactly by 2) ? Like in which spectrum the signals correlate the most? If you mean that, I looked into it, but the problem ist that its so lowfrequent because of the temperature. Maybe I did it wrong. For the crosscorrelation I used xcorr(signal1,signal2,0,'coeff'); , but the correlation between the speed of the vehicle(0,86) with Temp is nearly as high as the correlation between two temperaturesignals (0,99). Powerloss with Temp: 0,79. The powerloss should be the cause. Ill look into your options. – chris42 Nov 2 '16 at 10:39