Last Modified: March 15, 2017

Computes the inverse fast Hartley transform of a sequence.

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* = 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.

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

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 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.

**Default: **No error

The inverse Hartley transform of the input sequence.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**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.

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}**.

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: This product does not support FPGA devices