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.

The Hadamard matrix and Hadamard transform are fundamental problem-solving tools used in a wide spectrum of scientific disciplines and technologies including communication systems, signal and image processing (signal representation, coding, filtering, recognition, and watermarking), and digital logic (Boolean function analysis and synthesis, and fault-tolerant system design). They are thus a key component of modern information technology. In communication, the most important applications include error-correcting codes, spreading sequences, and cryptography. Other relevant applications include analysis of stock market data, combinatorics, experimental design, quantum computing, environmental monitoring, and many problems in chemistry, physics, optics, and geophysical analysis.

Hadamard matrices have attracted close attention in recent years, owing to their numerous known and new promising applications. In 1893, Jacques Hadamard conjectured that for any integer m divisible by 4, there is a Hadamard matrix of the order m. Despite the efforts of a number of individuals, this conjecture remains unproved, even though it is widely believed to be true. Historically, the problem goes back to James Joseph Sylvester in 1867.

The purpose of this book is to bring together different topics concerning current developments in Hadamard matrices, transforms, and their applications. Hadamard Transforms distinguishes itself from other books on the same topic because it achieves the following:

This book is suitable for a wide variety of audiences, including graduate students in electrical and computer engineering, mathematics, or computer science. Hadamard Transforms will prepare the reader for further exploration and support aspiring researchers in the field. The reader is not presumed to have a sophisticated mathematical background, but some mathematical familiarity is helpful.

Sos Agaian

Hakob Sarukhanyan

Karen Egiazarian

Jaakko Astola

July 2011