A Class Of Fractional Orthogonal Transforms And Their Applications

Along with the improvement of the research, the signal processed has developed from the steady signal to the non-steady signal. The ordinary Fourier transform has gradually exposed the limitation of studying problems of this kind:it is unable to attribute the time-frequency characteristic of the signal, which is exactly most important and the essential nature of the non-steady signal. In order to overcome this limitation, people have proposed the generalized form of Fourier transform:the fractional Fourier transformation. The fractional Fourier transform is considered to be the generalized form of the ordinary Fourier transform. It can change continuously from the time domain signal to the frequency domain signal, and has attracted more and more researchers'attention.The success of fractional Fourier transform enlightens people to study other fractional transforms. This paper derives the eigenvectors and eigenvalues sets of center weighted Hadamard transform matrix with the help of Kronecker product properties. After the cigen-values are obtained, we can use the eigen-decomposition method to define the fractional center weighted Hadamard transform. The proposed method can be extended to find the eigendecomposition of block center weighted Hadamard transform matrix. Then, the fractional block center weighted Hadamard transform are obtained using similar methods. The presented fractional center weighted Hadamard transform and fractional block center weighted Hadamard transform are general form of center weighted Hadamard transform and block center weighted Hadamard transform, respectively, which have additional free parameter, and with these free parameters they may find their places in many applications. Based on this, the paper also discusses two special form of orthogonal transforms, the COSHAD transform and the HADCOS transform, respectively. The fractional COSHAD and HADCOS transforms are defined using the same method.The simulation experimental results indicate the presented fractional transforms arc useful for signal and image processing. In the last part of this paper, a phase based palmprint recognition algorithm is introduced, using the fractional Fourier transform. The simulation experiment indicates this algorithm has a very good recognition effect.