How to find the DFT of the derivative of a function

In this section, we will see how to find the DFT of the derivative of the function.

How to do it…

Return the k^th derivative (or integral) of a periodic sequence x.

If x_j and y_j are Fourier coefficients of the periodic functions x and y, respectively, then:

y_j = pow(sqrt(-1)*j*2*pi/period, order) * x_j
y_0 = 0 if order is not 0.

The previous snippet is just an illustration.

Parameters

x: array_like. Input array. order: int, optional. The order of differentiation. Default order is 1. If order is negative, then integration is carried out under the assumption that x_0 == 0. period: float, optional. The assumed period of the sequence. Default is 2*pi.

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