Computes the fast Hilbert transform of the input sequence X. Details
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X is the input sequence. |
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Hilbert{X} is the Hilbert transform of the output sequence. |
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error returns any error or warning from the VI. Refer to Signal Processing Error Codes for more information about these conditions. |
The Hilbert transform of a function x(t) is defined as
.
Using Fourier identities, you can show the Fourier transform of the Hilbert transform of x(t) is
h(t) H(f) = - j sgn(f) X(f),
where x(t) X(f) is a Fourier transform pair and
The Fast Hilbert Transform VI performs the discrete implementation of the Hilbert transform with the aid of the FFT routines based upon the h(t) H(f) Fourier transform pair by taking the following steps.
You use the Hilbert transform to extract instantaneous phase information, obtain the envelope of an oscillating signal, obtain single-sideband spectra, detect echoes, and reduce sampling rates.
The output sequence Y = Inverse FFT [X] is complex and it is returned in one complex array: Y = (Yre,Yim).
![]() | Note Because the Fast Hilbert Transform VI sets the DC and Nyquist components to zero when the number of elements in the input sequence is even, you cannot always recover the original signal with an inverse Hilbert transform. The Hilbert transform works well with bandpass limited signals, which exclude the DC and the Nyquist components. |