Increase the accuracy of vector differentiation

Hello,

I am suppose to do data analysis, I should differentiate vectors and I do that using diff function in Matlab, I got approxmated results as figure shows. my question is how to find the differentation without rounding numbers, I suppose to have values as in the second picture.

[Chandler Hall]

The diff function does not calculate derivatives, but rather finite differences. So if g = diff(f) then g(x) = f(x+1) - f(x).

This is equivalent to the slope of the secant line between these points on the curve, which will only equal the slope of the tangent line as the distance between samples points goes to zero.

To calculate instantaneous derivatives from a finite series, you would need to fit some curve to the data which you could then analytically differentiate.

Answer 1

[Star Strider]

The best way to calculate the numerical derivative is with the gradient function.

Since differentiation amplifies noise, filtering the data first, perhaps with the Savitzky-Golay filter sgolayfilt function, may be necessary.