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bundles / scipy latest / scipy / fftpack / _pseudo_diffs / hilbert

function

scipy.fftpack._pseudo_diffs:hilbert

source: /scipy/fftpack/_pseudo_diffs.py :195

Signature

def   hilbert ( x _cache = <_thread._local object at 0x0000> )

Summary

Return Hilbert transform of a periodic sequence x.

Extended Summary

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.

Returns

y : ndarray

The transformed input.

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.

See also

scipy.signal.hilbert

Compute the analytic signal, using the Hilbert transform.

Aliases

  • scipy.fftpack.hilbert