Derivative of Temperature vs time data

I have a CSV file with temperature data and time. I am trying to model the dynamic response of the temperature sensor, to do so I want to take the derivative of the data. I have used the "diff" command but my data just looks messy.

[Torsten]

Maybe you have to smooth your data first. But we cannot tell because we don't have access to your data and we don't know how you applied "diff" on them.

[dpb]

Also, if the time intervals aren't exactly uniform, then you will get a more accurate response with

deriv=diff(temp)./diff(time);

That still won't solve the issue if there is noise in the data, but will help with non-uniform sampling if that's happening as in a polling-like sampling scheme rather than via a triggered A/D converter.

[Walter Roberson]

If your times are not equal step, then you probably want to use gradient

[Sam Chak]

Hi Ryan, the diff() function in MATLAB, when applied to the measured data, will return some values. But it does not magically give you a smooth and beautiful mathematical model, like dT/dt = f(T). Just for your info.

P.S. Same as gradient().

[dpb]

And, of course, it also presumes the times have been recorded with sufficient precision to be able to use them...one often finds a timestamp has been recorded but not with sufficient precision to be useful.

Answer 1

[charan]

Hi Ryan,

Here are some suggestions to calculate a smoother derivative of noisy data:

• Smoothing the data by using smoothing filters and moving averages can help reduce noise. Refer to the following documentation: https://www.mathworks.com/help/curvefit/smoothing-data.html
• Removing outliers from the data and normalizing the signal can help improve the derivative.
• Curve fitting can be done to the data to obtain a functional representation of the data and then differentiate the fitted curve to obtain a better derivative. Refer to the following documentation: https://www.mathworks.com/help/curvefit/example-differentiating-and-integrating-a-fit.html

The following MATLAB answer might be useful to you: https://www.mathworks.com/support/search.html/answers/253882-differentiating-a-noisy-position-signal.html