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Separation of Overlapping Linear Frequency Modulated (LFM) Signals Using the Fractional Fourier Transform

Cowell, DMJ and Freear, S (2010) Separation of Overlapping Linear Frequency Modulated (LFM) Signals Using the Fractional Fourier Transform. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 57 (10). 2324 - 2333 . ISSN 0885-3010

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Abstract

Linear frequency modulated (LFM) excitation combined with pulse compression provides an increase in SNR at the receiver. LFM signals are of longer duration than pulsed signals of the same bandwidth; consequently, in many practical situations, maintaining temporal separation between echoes is not possible. Where analysis is performed on individual LFM signals, a separation technique is required. Time windowing is unable to separate signals overlapping in time. Frequency domain filtering is unable to separate signals with overlapping spectra. This paper describes a method to separate time-overlapping LFM signals through the application of the fractional Fourier transform (FrFT), a transform operating in both time and frequency domains. A short introduction to the FrFT and its operation and calculation are presented. The proposed signal separation method is illustrated by application to a simulated ultrasound signal, created by the summation of multiple time-overlapping LFM signals and the component signals recovered with +/-0.6% spectral error. The results of an experimental investigation are presented in which the proposed separation method is applied to time-overlapping LFM signals created by the transmission of a LFM signal through a stainless steel plate and water-filled pipe.

Item Type: Article
Copyright, Publisher and Additional Information: © 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works
Keywords: Pulse-Compression, Chirp Signals
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Electronic & Electrical Engineering (Leeds) > Institute of Integrated Information Systems (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 25 Jul 2011 10:43
Last Modified: 21 Nov 2014 11:44
Published Version: http://dx.doi.org/10.1109/TUFFC.2010.1693
Status: Published
Publisher: IEEE-Institute of Electrical Electronics Engineers
Identification Number: 10.1109/TUFFC.2010.1693
URI: http://eprints.whiterose.ac.uk/id/eprint/43139

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