title: Separation of overlapping linear frequency modulated (LFM) signals using the fractional fourier transform.
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.
authors.affiliation: Ultrasound Group, School of Electronicand Electrical Engineering, University of Leeds, Leeds, England. d.m.j.cowell@leeds.ac.uk
authors.forename: David M J
authors.initials: DM
authors.lastname: Cowell
authors.forename: Steven
authors.initials: S
authors.lastname: Freear
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005583:Fourier Analysis; D012815:Signal Processing, Computer-Assisted; D014463:Ultrasonography / Q000379:methods*