bundles / scipy latest / scipy / fftpack / _pseudo_diffs / hilbert
function
scipy.fftpack._pseudo_diffs:hilbert
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_likeThe input array, should be periodic.
_cache: dict, optionalDictionary that contains the kernel used to do a convolution with.
Returns
y: ndarrayThe 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