InverseDiscreteHadamardTransform

InverseDiscreteHadamardTransform[coef] returns the inverse discrete Hadamard transform (IDHT) of a list of DHT coefficients coef.

The 1D IDHT of a sequence X[k] is defined as

for n = 0,1,...,N-1, with N=2^m.

The 2D IDHT of a sequence X[k₁,k₂] is defined as

for n₁= 0, 1, ... , N₁-1 and n₂ = 0, 1,..., N₂-1, where N₁ = 2^m₁, N₂=2^m₂ and b_i(z) is the ith bit in the binary representation of z. The addition of the bits b_i in the exponent of -1 is in modulo-2 arithmetic. Note that the forward and inverse Hadamard transforms are identical.

The option SequencyOrdered → True returns the ordered form of the Hadamard transform. The default value is SequencyOrdered → False.

The argument coef may be a vector or a matrix.

See also User's Guide 8.5.

Example

This loads the package.

In[1]:=

This creates a list of Hadamard coefficients.

In[2]:=

Out[2]=

This computes the inverse Hadamard transform and verifies invertibility.

In[3]:=

Out[3]=

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