gives the discrete Hadamard transform of list.

Details and OptionsDetails and Options

  • The discrete Hadamard transform of a list of length is by default defined to be , where , is the ^(th) 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 an option . Sequency is the number of zero crossings of the Hadamard basis sequences. The default is "SequencyOrdered"->True, where the sequency increases with row or column index. With "SequencyOrdered"->False, .
  • The forward and inverse Hadamard transforms are identical.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Discrete Hadamard transform of a list:

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Inverse discrete Hadamard transform:

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Discrete Hadamard transform of a 2D sequence that depicts a white rectangle on a black background:

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Introduced in 2012