# scipy.fftpack.hilbert¶

scipy.fftpack.hilbert(x, _cache={})[source]

Return Hilbert transform of a periodic sequence x.

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

y_j = sqrt(-1)*sign(j) * x_j
y_0 = 0

Parameters: x : array_like The input array, should be periodic. _cache : dict, optional Dictionary that contains the kernel used to do a convolution with. y : ndarray The transformed input.

scipy.signal.hilbert
Compute the analytic signal, using the Hilbert transform.

Notes

If sum(x, axis=0) == 0 then hilbert(ihilbert(x)) == x.

For even len(x), the Nyquist mode of x is taken zero.

The sign of the returned transform does not have a factor -1 that is more often than not found in the definition of the Hilbert transform. Note also that scipy.signal.hilbert does have an extra -1 factor compared to this function.

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