Inverse Fast Hilbert Transform (Not in Base Package)

Computes the inverse fast Hilbert transform of the input sequence using Fourier identities. Details

X is the input signal.
Inv Hilbert {X} is the Hilbert Transform of the input signal X.
error returns any error or warning from the VI. Refer to Signal Processing Error Codes for more information about these conditions.

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

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.

  1. Hilbert transform the input sequence X
    Y = H{X}.
  2. Negate Y to obtain the inverse Hilbert transform
    .

The Hilbert transform works best with AC coupled, band-limited signals.