Hadamard transforms

Hadamard transforms [electronic resource] / Sos Agaian [and others]

The Hadamard matrix and Hadamard transform are fundamental problem-solving tools in a wide spectrum of scientific disciplines and technologies, such as communication systems, signal and image processing (signal representation, coding, filtering, recognition, and watermarking), digital logic (Boolean...

Full description

Saved in:
Bibliographic Details
Online Access: Full Text (via SPIE Digital Library)
Corporate Author: SPIE (Society)
Other Authors: Agaian, S. S.
Format: Electronic eBook
Language:English
Published: Bellingham, Wash. : SPIE Press, 2011.
Subjects:
Hadamard matrices.
Table of Contents:
  • 1. Classical Hadamard matrices and arrays
  • Sylvester or Walsh-Hadamard matrices
  • Walsh-Paley matrices
  • Walsh and related systems
  • Walsh system
  • Cal-Sal orthogonal system
  • The Haar system
  • Hadamard matrices and related problems
  • Complex Hadamard matrices
  • Complex Sylvester-Hadamard transform
  • Complex Walsh-Hadamard transform
  • Complex Paley-Hadamard transform
  • Complex Walsh transform
  • References.
  • 2. Fast classical discrete orthogonal transforms
  • Matrix based fast dots algorithms
  • Fast Walsh-Hadamard transform
  • Fast Walsh-Paley transform
  • Cal-Sal fast transform
  • Fast complex Hadamard transform
  • Fast Haar transform
  • References.
  • 3. Discrete orthogonal transforms and Hadamard matrices
  • Fast discrete orthogonal transforms via Walsh-Hadamard transform
  • Fast Fourier transform implementation
  • Fast Hartley transform
  • Fast cosine transform
  • Fast Haar transform
  • Integer slant transforms
  • Slant-Hadamard transforms
  • Parametric slant-Hadamard transform matrices
  • Construction of sequential integer slant-Hadamard transforms
  • Fast algorithms
  • Examples of slant transform matrices
  • Construction of the iterative parametric slant-Haar transform
  • References.
  • 4. "Plug in template" method: Williamson-Hadamard matrices
  • Williamson-Hadamard matrices
  • Construction of eight Williamson matrices
  • Williamson matrices from regular sequences
  • References.
  • 5. Fast Williamson-Hadamard transforms
  • Construction of Hadamard matrices using Williamson matrices
  • Parametric Williamson matrices and block representation of Williamson-Hadamard matrices
  • Fast block Williamson-Hadamard transform
  • Multiplicative theorem based Williamson-Hadamard matrices
  • Multiplicative theorem based fast Williamson-Hadamard transforms
  • Complexity and comparison
  • Complexity of block-cyclic block-symmetric Williamson-Hadamard transform
  • Complexity of Hadamard transform from multiplicative theorem
  • References.
  • 6. Skew Williamson-Hadamard transforms
  • Skew Hadamard matrices
  • Skew-symmetric Williamson matrices
  • Block representation of skew-symmetric Williamson-Hadamard matrices
  • Fast block-cyclic skew-symmetric Williamson-Hadamard transform
  • Block-cyclic skew-symmetric fast Williamson-Hadamard transform in add/shift architectures
  • References.
  • 7. Decomposition of Hadamard matrices
  • Decomposition of Hadamard matrices by (+1,-1) vectors
  • Decomposition of Hadamard matrices and their classification
  • Multiplicative theorems of orthogonal arrays and Hadamard matrices construction
  • References.
  • 8. Fast Hadamard transforms for arbitrary orders
  • Hadamard matrix construction algorithms
  • Hadamard matrix vector representation
  • Fast Hadamard transform of order N = 0(mod 4)
  • Fast Hadamard transform via four vector representation
  • Fast Hadamard transform of order N = 0(mod 4) on shift/add architectures
  • Complexities of developed algorithms
  • Complexity of the general algorithm
  • Complexity of the general algorithm with shifts
  • References.
  • 9. Orthogonal arrays
  • Orthogonal designs
  • Baumert-Hall arrays
  • A-matrices
  • Geothals-Seidel arrays
  • Plotkin arrays
  • Welch arrays
  • References.
  • 10. Higher dimensional Hadamard matrices
  • Three dimensional Hadamard matrices
  • Three dimensional Williamson-Hadamard matrices
  • 3D Hadamard matrices of order 4n+2
  • Fast 3D Walsh Hadamard transforms
  • Operations with higher dimensional complex matrices
  • 3D complex Hadamard transforms
  • Construction of high-dimensional generalized Hadamard matrices
  • References.
  • 11. Extended Hadamard matrices
  • Generalized Hadamard matrices
  • Introduction and statement of problems
  • Some necessary conditions of generalized Hadamard matrices existence
  • Construction of generalized Hadamard matrices of new orders
  • Generalized Yang matrices and construction of generalized Hadamard matrices
  • Chrestenson transform
  • The Rademacher-Walsh transforms
  • Chrestenson functions and matrices
  • Chrestenson transforms algorithms
  • Chrestenson transform of order 3n
  • Chrestenson transform of order 5n
  • Fast generalized Haar transforms
  • The generalized Haar functions
  • 2n-point Haar transform
  • 3n-point generalized Haar transform
  • 4n-point generalized Haar transform
  • 5n-point generalized Haar transform
  • References.
  • 12. Jacket Hadamard matrices
  • Introduction to jacket matrices
  • Weighted Sylvester-Hadamard matrices
  • Parametric reverse jacket matrices
  • Construction of special type parametric reverse jacket matrices
  • Fast parametric reverse jacket transform
  • Fast 4x4 parametric reverse jacket transform
  • Fast 8x8 parametric reverse jacket transform
  • References.
  • 13. Applications of Hadamard matrices in communication systems
  • Hadamard matrices and communication systems
  • Overview of error-correcting codes
  • Levenshtein constructions
  • Uniquely decodable base codes
  • Shortened codes construction and application to data coding and decoding
  • Space-time codes from Hadamard matrices
  • The general wireless system model
  • Orthogonal array and linear processing design
  • Design of space-time codes from Hadamard matrix
  • References.
  • 14. Randomization of discrete orthogonal transforms and encryption
  • Preliminaries
  • Matrix forms of DHT, DFT, DCT, and other DOTs
  • Cryptography
  • Randomization of discrete orthogonal transforms
  • The theorem of randomizations of discrete orthogonal transforms
  • Discussions on the square matrices P and Q
  • Examples of randomized transform matrix Ms
  • Transform properties and features
  • Examples of randomized discrete orthogonal transforms
  • Encryption applications
  • 1D data encryption
  • 2D data encryption and beyond
  • Examples of image encryption
  • Key space analysis
  • Confusion property
  • Diffusion property.
  • Appendix
  • A.1. Elements of matrix theory
  • A.2. First rows of cyclic symmetric Williamson type matrices of order n, N = 3, 5 ..., 33, 37, 39, 41, 43, 49, 51, 55, 57, 61, 63
  • A.3. First block-rows of the block-cyclic block-symmetric Williamson-Hadamard matrices of order 4n, n = 3, 5 ..., 33, 37, 39, 41, 43, 49, 51, 55, 57, 61, 63
  • A.4. First rows of cyclic skew-symmetric Williamson type matrices of order n, n = 3, 5 ..., 33, 35
  • A.5. First block-rows of skew-symmetric block Williamson-Hadamard matrices of order 4n, n = 3, 5 ..., 33, 35.

Similar Items