Open AccessBook
The Fractional Fourier Transform: with Applications in Optics and Signal Processing
TLDR
The fractional Fourier transform (FFT) as discussed by the authors has been used in a variety of applications, such as matching filtering, detection, and pattern recognition, as well as signal recovery.Abstract:
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.read more
Citations
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Journal ArticleDOI
Generalized convolution theorem associated with fractional Fourier transform
TL;DR: The ordinary convolution theorem and some of its existing extensions related to the FRFT are shown to be special cases of thederived results, and some applications of the derived results are presented.
Journal ArticleDOI
Paraxial speckle-based metrology systems with an aperture
Damien P. Kelly,Jennifer E. Ward,Bryan M. Hennelly,Unnikrishnan Gopinathan,Feidhlim T. O'Neill,John T. Sheridan +5 more
TL;DR: This work extends the OFRT analysis to more general LCT systems with a single limiting aperture and demonstrates the benefits of using an LCT approach to metrology design by showing that by varying the curvature of the illuminating field, it can effectively change the output domain.
Journal ArticleDOI
Fractional Fourier transform based features for speaker recognition using support vector machine
TL;DR: This paper presents a text-independent speaker recognition technique in which the conventional Fourier transform in Mel-Frequency Cepstral Coefficient front-end is substituted by fractional Fourier Transform, making the technique robust against additive noise compared to Fourier domain maintaining same computational complexity.
Journal ArticleDOI
The ambiguity function associated with the linear canonical transform
TL;DR: In this paper, a new ambiguity function (AF) associated with the linear canonical transform (LCT) is proposed, this new AF is defined based on the LCT and the classical AF and is applied to detect the parameters of the linear frequency modulated signals by combining with the classical Radon transform.
Patent
Optical beam routing apparatus and methods
TL;DR: In this paper, the authors describe an optical beam routing apparatus consisting of at least one optical input to receive an input beam, a plurality of optical outputs, a spatial light modulator (SLM) on an optical path between said optical input and said optical outputs; and a driver for said SLM to display a kinoform on the SLM in order to diffract said input beam into an output beam.