# Inverse Fast Hilbert Transform (G Dataflow)

Version:

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

## reset

A Boolean that specifies whether to reset the internal state of the node.

 True Resets the internal state of the node. False Does not reset the internal state of the node.

This input is available only if you wire a double-precision, floating-point number to Hilbert{x}.

Default: False

## Hilbert{x}

Input signal.

This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

## sample length

Length of each set of data. The node performs computation for each set of data.

sample length must be greater than zero.

This input is available only if you wire a double-precision, floating-point number to Hilbert{x}.

Default: 100

## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## x

The inverse Hilbert Transform of the input signal.

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm for Calculating the Inverse Fast Hilbert Transform

The following equation defines the continuous inverse Hilbert transform of a function h(t):

$x\left(t\right)={H}^{-1}\left\{h\left(t\right)\right\}=-\frac{1}{\pi }{\int }_{-\infty }^{\infty }\frac{h\left(\tau \right)}{t-\tau }d\tau$

Using the definition of the continuous Hilbert transform

$h\left(t\right)=H\left\{x\left(t\right)\right\}=\frac{1}{\pi }{\int }_{-\infty }^{\infty }\frac{x\left(\tau \right)}{t-\tau }d\tau$

you can obtain the continuous inverse Hilbert transform by negating the forward Hilbert transform

$x\left(t\right)={H}^{-1}\left\{h\left(t\right)\right\}=-H\left\{h\left(t\right)\right\}$

This node performs the discrete inverse Hilbert transform with the aid of the continuous Hilbert transform by taking the following steps:

1. Calculate the discrete Hilbert transform of the input sequence X.
Y = H{X}

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

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

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application