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A Class of Fractional Orthogonal Transforms and Their Applications

Author: NieZongFeng
Tutor: ZhuHongQing
School: East China University of Science and Technology
Course: Signal and Information Processing
Keywords: Center Weighted Hadamard transform Kronecker product Fractional Block COSHAD transform HADCOS transform
CLC: TN911.7
Type: Master's thesis
Year: 2012
Downloads: 23
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Abstract


With the deepening of scientific research, the signal has been handled by the stationary signal to the overall transformation of non-stationary signals, traditional Fourier transform method gradually exposed the limitations of the study of such problems: they can not characterize the signal when frequency characteristics, and this characteristic is precisely the non-stationary signals the most important and the most the nature of the wood. To overcome this limitation, the fractional Fourier transform, fractional Fourier transform is well characterized by the correspondence between the different time and a different frequency. Fractional transform generalized form of ordinary transform can continuously change signal from the time domain to the frequency domain signal, is an important means of time-frequency analysis, subject to the attention of a growing number of researchers in recent years. The the Discrete Hadamard transform family is an important class of transform analysis method, mainly used in digital image processing and signal encoding, currently a hot research direction Fractional Hadamard transform. This paper presents a Fractional Center Weighted Hadamard transform defined Kronecker product. Characteristic vectors and the help of Kronecker product of nature, center weighted Hadamard transform matrix eigenvalue decomposition, and then use the resulting value is defined Fractional center weighted Hadamard transform matrix, and then gives the of a Fractional center weighted Hadamard transform defined. After the study found, the so defined Fractional center weighted Hadamard transform to meet the basic nature Fractional transform, transform the order additive. Block center weighted Hadamard transform is an important class of Hadamard transform, this article also gives the definition and nature of a Fractional block center weighted Hadamard transform. Based on this discussion, but also introduced two special forms of discrete orthogonal transformation, respectively for COSHAD transform and HADCOS transform is given the Fractional the COSHAD transforms and fractional HADCOS of transformation definition, used the same method Kronecker product , defined as the fractional transform is a generalized form of the corresponding ordinary transform. Fractional transform one more free parameter than the ordinary form of transformation - transform the order, so that has a good prospect of application in many areas such as signal and image processing. The article concludes with a discussion of a fractional transform in phase palmprint identification algorithms, simulation shows that the algorithm has good recognition.

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