DiscreteHadamardTransform
DiscreteHadamardTransform[list]
gives the discrete Hadamard transform of list.
Details and Options

- DiscreteHadamardTransform is also known as Walsh transform and Walsh-Hadamard transform.
- The discrete Hadamard transform
of a list
of length
is by default defined to be
, where
,
is the
bit in the binary representation of the integer
, and
.
- DiscreteHadamardTransform returns a list that has a power of 2 length. If the length of the input list is not a power of 2, it is zero padded to a length that is the smallest power of 2 greater than
.
- DiscreteHadamardTransform takes a Method option. Possible settings are "BitComplement" and "Sequency" (default).
- The forward and inverse Hadamard transforms are identical. »
Examples
open allclose allBasic Examples (2)
Options (1)
Applications (1)
Properties & Relations (3)
The Hadamard transform is its own inverse (an involution):
DiscreteHadamardTransform automatically pads with zeros to the nearest power of 2:
Text
Wolfram Research (2012), DiscreteHadamardTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteHadamardTransform.html (updated 2014).
CMS
Wolfram Language. 2012. "DiscreteHadamardTransform." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/DiscreteHadamardTransform.html.
APA
Wolfram Language. (2012). DiscreteHadamardTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiscreteHadamardTransform.html