Hadamard transforms

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.

"SPIE vol. no.: PM207"--Page 4 of cover.

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 tra…