Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Fast Walsh-Hadamard transform

`y = fwht(x)`

y = fwht(x,n)

y = fwht(x,n,ordering)

`y = fwht(x)`

returns the coefficients of
the discrete Walsh-Hadamard transform of the input `x`

.
If `x`

is a matrix, the FWHT is calculated on each
column of `x`

. The FWHT operates only on signals
with length equal to a power of 2. If the length of `x`

is
less than a power of 2, its length is padded with zeros to the next
greater power of two before processing.

`y = fwht(x,n)`

returns the `n`

-point
discrete Walsh-Hadamard transform, where `n`

must
be a power of 2. `x`

and `n`

must
be the same length. If `x`

is longer than `n`

, `x`

is
truncated; if `x`

is shorter than `n`

, `x`

is
padded with zeros.

`y = fwht(x,n,ordering)`

specifies the ordering
to use for the returned Walsh-Hadamard transform coefficients. To
specify the ordering, you must enter a value for the length `n`

or,
to use the default behavior, specify an empty vector (`[]`

)
for `n`

. Valid values for the ordering are the following:

Ordering | Description |
---|---|

`'sequency'` | Coefficients in order of increasing sequency value, where each row has an additional zero crossing. This is the default ordering. |

`'hadamard'` | Coefficients in normal Hadamard order. |

`'dyadic'` | Coefficients in Gray code order, where a single bit change occurs from one coefficient to the next. |

For more information on the Walsh functions and ordering, see Walsh-Hadamard Transform.

[1] Beauchamp, Kenneth G. *Applications
of Walsh and Related Functions: With an Introduction to Sequency Theory*.
London: Academic Press, 1984.

[2] Beer, Tom. "Walsh Transforms." *American
Journal of Physics*. Vol. 49, 1981, pp. 466–472.

Was this topic helpful?