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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.
Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on (Volume:57 , Issue: 10 )
Date of Publication: October 2010