Last Modified: January 9, 2017

Computes the real Walsh Hadamard transform of a sequence.

The input sequence.

The length of the sequence has to be a power of 2, otherwise this node returns an error.

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

**Default: **No error

The Walsh Hadamard transform of the input sequence.

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