# Inverse FHT (G Dataflow)

Computes the inverse fast Hartley transform of a sequence.  ## 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 Hartley{x}.

Default: False ## Hartley{x}

The input sequence.

To properly compute the inverse FHT of Hartley{x}, the number of elements, n, in the sequence must be a valid power of 2.

n = 2m

for m = 1, 2, 3,...,23

If the number of elements in Hartley{x} is not a valid power of 2, the node sets x to an empty array and returns an error.

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 Hartley{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 Hartley transform of the input sequence. ## 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 Computing the Inverse Fast Hartley Transform

The inverse Hartley transform of a function X(f) is defined by the following equation:

$x\left(t\right)={\int }_{-\infty }^{\infty }X\left(f\right)\mathrm{cas}\left(2\pi ft\right)df$

where $\mathrm{cas}\left(x\right)=\mathrm{cos}\left(x\right)+\mathrm{sin}\left(x\right)$.

If Y represents the output sequence x, this node calculates Y through the discrete implementation of the inverse Hartley integral

${Y}_{k}=\frac{1}{n}\underset{i=0}{\overset{n-1}{\sum }}{X}_{i}\mathrm{cas}\frac{2\pi ik}{n}$

for k = 1, 2, ...n - 1,

where n is the number of elements in Hartley{x}.

## Comparing the Inverse Hartley Transform with the Inverse Fourier Transform

The inverse Hartley transform maps real-valued frequency sequences into real-valued sequences. You can use it instead of the inverse Fourier transform to convolve, deconvolve, and correlate signals. You also can derive the Fourier transform from the Hartley transform.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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