Hadamard transforms / Sos S. Agaian, Hakob G. Sarukhanyan, Karen O. Egiazarian, Jaakko Astola.

• 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 --. 
• 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 --. 
• 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 --. 
• 4. "Plug in template" method: Williamson-Hadamard matrices -- Williamson-Hadamard matrices -- Construction of eight Williamson matrices -- Williamson matrices from regular sequences --. 
• 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 --. 
• 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 --. 
• 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 --. 
• 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 --. 
• 9. Orthogonal arrays -- Orthogonal designs -- Baumert-Hall arrays -- A-matrices -- Geothals-Seidel arrays -- Plotkin arrays -- Welch arrays --. 
• 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 --. 
• 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 --. 
• 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 --. 
• 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 --. 
• 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.

• 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 function analysis and synthesis), and fault-tolerant system design. Hadamard Transforms intends to bring together different topics concerning current developments in Hadamard matrices, transforms, and their applications. Each chapter begins with the basics of the theory, progresses to more advanced topics, and then discusses cutting-edge implementation techniques. The book covers a wide range of problems related to these matrices/transforms, formulates open questions, and points the way to potential advancements. Hadamard Transforms is suitable for a wide variety of audiences, including graduate students in electrical and computer engineering, mathematics, or computer science. Readers are not presumed to have a sophisticated mathematical background, but some mathematical background is helpful. This book will prepare readers for further exploration and will support aspiring researchers in the field. 

Ämnesord

Hadamard matrices.  (LCSH)

Genre

Electronic books.  (LCSH)

Indexterm och SAB-rubrik

Tche Linjär och multilinjär algebra

Klassifikation

QA166.4 (LCC)

512.9434 (DDC)

Tche (kssb/8)