Why level of noise can be magnified twice through each numerical differentiation?

1. Why does differentiation increase noise?
2. Does differentiation amplify noise?
3. How do you differentiate a signal in Matlab?

Why does differentiation increase noise?

Another reason is that by differentiating, you remove the low-frequency components, so your eyes see mostly the high-frequency components giving you the impression of having more noise.

Does differentiation amplify noise?

It is often said that "differentiation increases the noise". That is true, but it is not the main problem.

How do you differentiate a signal in Matlab?

You want to differentiate a signal without increasing the noise power. MATLAB®'s function diff amplifies the noise, and the resulting inaccuracy worsens for higher derivatives. To fix this problem, use a differentiator filter instead.