Version:

Last Modified: June 25, 2019

Computes the real Walsh Hadamard transform of a sequence.

The input sequence.

The length of the sequence must be a power of 2, otherwise this node 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 **x**.

**Default: **128

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 Walsh Hadamard 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 Walsh Hadamard transform is based on an orthogonal system consisting of functions of only two elements -1 and 1. For the
special case of *n* = 4, the Walsh Hadamard transform of the signal *X* = {*x*_{0}, *x*_{1}, *x*_{2}, *x*_{3}} can be noted in the following matrix form:

$WH\left\{X\right\}=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& -1& 1& -1\\ 1& 1& -1& -1\\ 1& -1& -1& 1\end{array}\right]\left[\begin{array}{c}{\begin{array}{c}x\end{array}}_{0}\\ {x}_{1}\\ {x}_{2}\\ {x}_{3}\end{array}\right]$

If
*WH*_{n
}and
*WH*_{n+1} denote the Walsh Hadamard matrices of dimension 2^{n} and 2^{n + 1} respectively, the rule is

${WH}_{n+1}=\left[\begin{array}{cc}{WH}_{n}& {WH}_{n}\\ {WH}_{n}& {-WH}_{n}\end{array}\right]$

where -*WH*_{n} is meant in the element wise sense.

The Walsh Hadamard transform has similar properties to the Fourier transform, but the computational effort is considerably smaller.

The following diagram shows the Walsh Hadamard transform of a pulse pattern signal of length 256, delay 32, and width 64.

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported

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