Version:

Last Modified: June 25, 2019

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

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

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: Not supported

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