Smoothing Numerical Differentiation Result

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Ahmed Zankoor 2018-4-23

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评论： Ahmed Zankoor 2018-4-26

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I want to get the derivative of this S-shaped curve this way (x*(dy/dx)) which is expected to be like the normal distribution bell-shaped curve, I used x(2:end).*diff(y)./diff(x) , gradient function and central difference method. but the result was very noisy since it is a numerical differentiation. My question, is there a way to smooth the result to get a better derivative curve?

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Jim Riggs 2018-4-23

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编辑：Jim Riggs 2018-4-23

Numerical Derivative Formulas.pdf

The attached file contains some higher-order methods for computing numerical derivatives. You can start with this. For very well behaved data, further smoothing might be achieved by curve fitting a function to the data and using the function derivative. If a more general method is desired, there are a number of ways to filter noisy data (for example, Matlab function "filter").

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Ahmed Zankoor 2018-4-25

The problem that I can not understand is that the data I want to find the derivative for is not that noisy yet I get a bad derivative, you can see the attached figures. So I do not think it needs filtering.

Ahmed Zankoor 2018-4-26

I found the problem, the x variable is generated using normrnd (random variables following normal distribution) and the differences between the values vary greatly. for example dx=[.2 .01 ...] that is why when we compute the derivative its values show heavy noise.

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