# scipy.fftpack.diff¶

scipy.fftpack.diff(x, order=1, period=None, _cache={})[source]

Return kth derivative (or integral) of a periodic sequence x.

If x_j and y_j are Fourier coefficients of 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.

Parameters
xarray_like

Input array.

orderint, 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.

periodfloat, optional

The assumed period of the sequence. Default is 2*pi.

Notes

If sum(x, axis=0) = 0 then diff(diff(x, k), -k) == x (within numerical accuracy).

For odd order and even len(x), the Nyquist mode is taken zero.

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