Fractional Fourier transform as a signal processing tool: An overview of recent developments <s> Applications <s> Preface. Acknowledgments. Introduction. 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 Works. Credits. Index. <s> BIB001 </s> Fractional Fourier transform as a signal processing tool: An overview of recent developments <s> Applications <s> Signal processing can be found in many applications and its primary goal is to provide underlying information on specific problems for the purpose of decision making. Traditional signal processing approaches assume the stationarity of signals, which in practice is not often satisfied. Hence, time or frequency descriptions alone are insufficient to provide comprehensive information about such signals. On the contrary, time-frequency analysis is more suitable for nonstationary signals. Therefore, this paper provides a status report of feature based signal processing in the time-frequency domain through an overview of recent contributions. The feature considered here is energy concentration. The paper provides an analysis of several classes of feature extractors, i.e., time-frequency representations, and feature classifiers. The results of the literature review indicate that time-frequency domain signal processing using energy concentration as a feature is a very powerful tool and has been utilized in numerous applications. The expectation is that further research and applications of these algorithms will flourish in the near future. <s> BIB002
In this section, we review the practical applications of the FRFT and its discrete counterpart as a signal processing tool. Nevertheless, our literature review showed that applications are very scarce beyond optics. We anticipate additional publications regarding practical applications of the FRFT are bound to appear. For example, we foresee an increased number of applications of the FRFT based timefrequency representations in speech and music processing, biomedical signal processing, and mechanical vibrations analysis. Some problems stemming from such applications demand such advanced time-frequency representations (e.g., spectrogram, WD), since these classical time-frequency tools do not provide a framework sufficient for a comprehensive analysis BIB002 . It should be also mentioned that in this paper we devote more space to newer applications of the FRFT such as watermarking and communications. Other contributions (e.g., BIB001  ) described either more traditional applications such as filtering and signal recovery or only briefly covered different applications. Our goal is to emphasize that the FRFT is a valuable tool in many various applications.