Enable JavaScript to interact with content and submit forms on Wolfram websites. Learn how

Legacy Documentation

Digital Image Processing (2000)

This is documentation for an obsolete product.

Current products and services

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]=