Practical Applications of the Fractional Fourier Transform Using MatLab

This book will describe the Fractional Fourier Transform (FrFT), which is a highly useful signal processing tool, using simple mathematical equations, illustrations, and MatLab code with many examples. The first two chapters will provide a brief introduction and the mathematical background on the FrFT. The next chapters (Chapters 3-15) will describe new algorithms on the FrFT with detailed code and examples. These chapters will include several new applications and algorithms using the FrFT, including co-channel interference separation for communications, speech processing, modulation, channel estimation, echo separation in radar, enhancements in digital image watermarking, and twin fetal heartbeat separation. Chapter 16 describes an FrFT Spectrum Analyzer hardware concept.

1. The book applies a single technique, the Fractional Fourier Transform (FrFT) to a wide array of technical fields, instead of discussing multiple techniques associated with a given field.

2. The book will arm the reader with a good grasp of the FrFT – what it is and what it can do.

3. By providing examples across a wide range of fields from communications to image processing, from seismology to biomedical, we can reach a wide readership. We provide tools to enhance signal processing applications in all these fields.

4. By providing uses of the FrFT across multiple fields, we hope to provide an understanding of the potential for such signal processing methods to open the door for others to advance the research in their particular fields and possibly extend the applications to other fields that have not yet been explored or considered.

5. We hope that readers working in the fields of communications, radar, GPS, etc. will employ the tools that have been developed, thereby leading to new prototypes, new hardware, and even more applications.

6. We hope to get readers in one field potentially interested in other fields, thereby increasing their breadth and getting them excited about a new subject matter.