The Fractional Fourier Transform: Applications in Optics and Signal Processing

Background material introduces time frequency analysis emphasizing the Wigner distribution, ambiguity function and canonical transforms.

Chapter on phase-space optics employs matrix algebra in a unified manner for both wave and geometrical optics, leading to many important results such as those on general Fourier transform planes and optical invariants.

Separate discussion of optics for readers with no interest in optics.

Unifying knowledge from the mathematics, optics, and signal processing literature in a manner accessible to a broad audience, this book is of interest to, researchers, engineers, and senior undergraduate and graduate students in electrical engineering, physics, and mathematics.

Contents

• Preface
• Acknowledgments
• Signals, systems, and transformations
• Wigner distributions and linear canonical transforms
• The fractional Fourier transform
• Time-order and space-order representations
• The discrete fractional Fourier transform
• Optical signals and systems
• Phase-space optics
• The fractional Fourier transform in optics
• Applications of the fractional Fourier transform to filtering, estimation, and signal recovery
• Applications of the fractional Fourier transform to matched filtering, detection, and pattern recognition
• Bibliography on the fractional Fourier transform
• Other cited books
• credits
• Index