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Inverse Fast Walsh–Hadamard transform


y = ifwht(x)
y = ifwht(x,n)
y = ifwht(x,n,ordering)


y = ifwht(x) returns the coefficients of the inverse discrete fast Walsh–Hadamard transform of the input x. If x is a matrix, the inverse fast Walsh-Hadamard tranform is calculated on each column of x. The inverse fast Walsh-Hadamard tranform 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 = ifwht(x,n) returns the n-point inverse discrete Walsh–Hadamard transform, where n must be a power of 2.

y = ifwht(x,n,ordering) specifies the ordering to use for the returned inverse Walsh–Hadamard transform coefficients. To specify 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 ordering are the following strings:

'sequency'Coefficients in order of ascending 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.

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The inverse fast Walsh-Hadamard tranform algorithm is similar to the Cooley-Tukey algorithm used for the inverse FFT. Both use a butterfly structure to determine the transform coefficients. See the references below for details.


[1] Beauchamp, K.G., Applications of Walsh and Related Functions, Academic Press, 1984.

[2] Beer, T., Walsh Transforms, American Journal of Physics, Volume 49, Issue 5, May 1981.

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