Digital Image Processing
Digital Signal Processing (4th Edition)
Digital Signal Processing (4th Edition)
A Recursive Algorithm for Sequency-Ordered Fast Walsh Transforms
IEEE Transactions on Computers
2-D and 1-D multipaired transforms: frequency-time type wavelets
IEEE Transactions on Signal Processing
Sequency-Ordered Complex Hadamard Transform: Properties, Computational Complexity and Applications
IEEE Transactions on Signal Processing - Part I
Multicomponent AM–FM Representations: An Asymptotically Exact Approach
IEEE Transactions on Audio, Speech, and Language Processing
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This paper presents a new transform known as natural-ordered complex Hadamard transform (NCHT) which is derived from the Walsh-Hadamard transform (WHT) through the direct block matrix operation. Some of its properties, including the exponential property of the NCHT and the shift invariant property of the NCHT power spectrum, are presented. The relationship of the NCHT with the sequency-ordered complex Hadamard transform (SCHT) is discussed. In fact, it is shown that NCHT is a natural-ordered version of complex Hadamard transform whereas SCHT shows the sequency ordering. This is parallel to their real-valued counterparts, the WHT and the sequency-ordered Walsh transform (SOWT). A fast algorithm for computing the NCHT is also developed using sparse matrix factorization and its computational complexity is examined.