Inverse Fast Hilbert Transform PtByPt (Not in Base Package)

Computes the Inverse Fast Hilbert Transform of the set of input data using Fourier Transform identities. Details

initialize, when TRUE, initializes the internal state of the VI.
input data is a set of input data.
sample length is the length of each set of incoming data. The VI performs computation on each set of data. The default is 100. sample length must be greater than zero.
Inverse Hilbert{X} is the inverse Hilbert transform of the set of input data.
error returns any error or warning condition from the VI. Refer to Point By Point Error Codes for more information about these conditions.

Inverse Fast Hilbert Transform PtByPt 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 VI performs the discrete implementation of the inverse Hilbert transform with the aid of the Hilbert transform by first performing the Hilbert transform of the input sequence X,

,

and then negating Y to obtain the inverse Hilbert transform,

.

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