| Linear frequency-modulated (LFM, chirp) signal, whose frequency changes over time, is often applied in ultrasonic signal. It is processed by Fourier transform in traditionally. But Fourier transform is a kind of overall transform, which can only describe signal in time or frequency domain and can not depict the time-frequency characters of the signal. While Fourier transform can only describe signal in time or frequency domain, Fractional Fourier transform (FRFT) can analysis signal in time-frequency domain. It is a new time-frequency analysis theory, representing signal in time-frequency plane where axes rotate an arbitrary angle counter- clockwise. FRFT is firstly applied in optical signal processing. After the discrete method was founded, it is used widely in electronic signal processing. Doing FRFT on chirp signal can improve the focus of the signal and ultrasound imaging quality.In this paper, we studied the definition, characteristics and applications of FRFT, including biomedical ultrasonic signal processing, Synthetic aperture sonar moving target detection, parameter estimation and moving target imaging. Our work includes: First, we investigated the principle and numerical implementation of FRFT, based on which we studied the detection and estimation of the chirp signal and the filtering of the chirp in the fractional domain. Then we set up a model of detection and parameter estimation of the chirp signal, using hierarchical iterative calculation algorithm in chirp signal detection. After that, we improved the match filter algorithm in fractional domain, using the filter model of the chirp signal in fractional Fourier domain. Our simulation results prove this by showing good performances with higher SNR, and improve ultrasound imaging quality. |
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