Hadamard matrices and their applications
Hadamard matrices and their applications
Hadamard matrix analysis and synthesis: with applications to communications and signal/image processing
Orthogonal Transforms for Digital Signal Processing
Orthogonal Transforms for Digital Signal Processing
A Concise Guide to Complex Hadamard Matrices
Open Systems & Information Dynamics
Digital Images Phase Encryption Using Fractional Fourier Transform
CERMA '06 Proceedings of the Electronics, Robotics and Automotive Mechanics Conference - Volume 01
Fast, Reliable & Secure Digital Communication Using Hadamard Matrices
ICCTA '07 Proceedings of the International Conference on Computing: Theory and Applications
Parametrizing complex Hadamard matrices
European Journal of Combinatorics
Discrete Fractional Fourier Transform Based on New Nearly Tridiagonal Commuting Matrices
IEEE Transactions on Signal Processing
Eigenvalues and eigenvectors of generalized DFT, generalized DHT,DCT-IV and DST-IV matrices
IEEE Transactions on Signal Processing
General multifractional Fourier transform method based on the generalized permutation matrix group
IEEE Transactions on Signal Processing
Fast Algorithms for the Computation of Sliding Discrete Hartley Transforms
IEEE Transactions on Signal Processing
Hadamard-based image decomposition and compression
IEEE Transactions on Information Technology in Biomedicine
Image scrambling without bandwidth expansion
IEEE Transactions on Circuits and Systems for Video Technology
Sequency-ordered generalized Walsh-Fourier transform
Signal Processing
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In this paper, a new class of reciprocal-orthogonal parametric (ROP) transforms having 3N/2 independent parameters for a sequence length N that is a power of two is proposed. The basic idea behind the proposed transforms is to appropriately combine a new parametric kernel with that of the well-known Walsh-Hadamard transform that results in a square parametric matrix operator of order N with some very interesting properties. It is shown that the inverse matrix operator of the proposed class of transforms can be easily obtained by taking the reciprocal of each of the entries of the forward matrix and then transposing the resulting matrix. In addition, a simple method is introduced in order to facilitate the generation of the matrix operator of the proposed ROP transforms. This method is then used specifically to construct new classes of unitary and multiplication-free transforms. Many other new transforms, as well some of the existing ones, can be derived from these proposed ROP transforms. An efficient algorithm is developed for a fast computation of the proposed transforms. In view of the availability of this fast algorithm and the property of easily computable inverse transform, the proposed ROP transforms can be used in many transform-based applications, with their independent parameters providing more degrees of freedom such as affording an additional secret key in watermarking and encryption applications.