Discrete fractional center weighted Hadamard transform

This paper derives the eigenvectors and eigenvalues sets of center weighted Hadamard transform (CWHT) matrix with the help of Kronecker product properties. After the eigenvalues are obtained, we can use the eigendecomposition method to define the fractional center weighted Hadamard transform (FrCWHT). The proposed method can be extended to find the eigendecomposition of block center weighted Hadamard transform (BCWHT) matrix. Then, the fractional block center weighted Hadamard transform (FrBCWHT) are obtained using similar methods. The presented FrCWHT and FrBCWHT are general form of CWHT and BCWHT, respectively, which have additional free parameter, and with these free parameters they may find their places in many applications. The final simulation experimental results indicate the FrCWHT and FrBCWHT are useful for signal and image processing.