Inverse Fast Hilbert Transform (DSP Module)
Computes the inverse fast Hilbert transform of the input sequence using Fourier identities.
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X is the first input sequence. |
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Inv Hilbert {X} is the inverse Hilbert Transform of the input signal X. |
Inverse Fast Hilbert Transform Details
The inverse Hilbert transform of a function h(t) is defined as
Using the definition of the Hilbert transform
you can obtain the inverse Hilbert transform by negating the forward Hilbert transform
x(t) = H–1{h(t)} = –H{h(t)}
Therefore, the Inverse Fast Hilbert Transform VI performs the discrete implementation of the inverse Hilbert transform with the aid of the Hilbert transform by taking the following steps.
- Hilbert transform the input sequence X
Y = H{X}. - Negate Y to obtain the inverse Hilbert transform
H–1{X} = –Y.
The Hilbert transform works best with AC coupled, band-limited signals.