# Inverse FHT (G Dataflow)

Version:

Computes the inverse fast Hartley transform of a sequence.

## Hartley{x}

The input sequence.

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

$n={2}^{m}$

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.

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

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.

## 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