The Use of Fractional Fourier Transform for the Extraction of Overlapped Harmonic Chirp Signals

In ultrasound harmonic imaging, high bandwidth is essential to provide good axial resolution at the receiver. However, increasing the bandwidth will cause overlapping amongst the nonlinear harmonic components. Conventional frequency domain filtering approach normally fails to extract the desired harmonic component under overlapped harmonic condition. The purpose of this work is to use broadband linear chirp signals for better SNR (Signal to Noise Ratio) andaxial resolution. Also on the receiving side, the FrFT (Fractional Fourier Transform) is used as a filtering tool to extract the overlapped second harmonic component from the nonlinear received signal. Pulse compression of the second harmonic chirp signal is also performed using the harmonic matched filter to restore axial resolution. Comparing the results of FrFT pre-filtered with unfiltered compressed signals; it is found that up to a 35.5dB RSLL (Reduction in Range Side Lobe Level) is realisable leading to an improved detection and image resolution