# scipy.fftpack.diff¶

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

Return k-th 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: 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.

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.

#### Previous topic

scipy.fftpack.idst

#### Next topic

scipy.fftpack.tilbert