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:
- xarray_like
The input array, should be periodic.
- _cachedict, optional
Dictionary that contains the kernel used to do a convolution with.
- Returns:
- yndarray
The transformed input.
See also
scipy.signal.hilbert
Compute the analytic signal, using the Hilbert transform.
Notes
If
sum(x, axis=0) == 0
thenhilbert(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.