scipy.fftpack.
hilbert#
- scipy.fftpack.hilbert(x, _cache=<_thread._local object>)[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) == 0then- 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.hilbertdoes have an extra -1 factor compared to this function.