Pulse compression of harmonic chirp signals using the fractional fourier transform

In ultrasound harmonic imaging with chirp-coded excitation, a harmonic matched filter (HMF) is typically used on the received signal to perform pulse compression of the second harmonic component (SHC) to recover signal axial resolution. Designing the HMF for the compression of the SHC is a problematic issue because it requires optimal window selection. In the compressed second harmonic signal, the sidelobe level may increase and the mainlobe width (MLW) widen under a mismatched condition, resulting in loss of axial resolution. We propose the use of the fractional Fourier transform (FrFT) as an alternative tool to perform compression of the chirp-coded SHC generated as a result of the nonlinear propagation of an ultrasound signal. Two methods are used to experimentally assess the performance benefits of the FrFT technique over the HMF techniques. The first method uses chirp excitation with central frequency of 2.25 MHz and bandwidth of 1 MHz. The second method uses chirp excitation with pulse inversion to increase the bandwidth to 2 MHz. In this study, experiments were performed in a water tank with a single-element transducer mounted coaxially with a hydrophone in a pitch-catch configuration. Results are presented that indicate that the FrFT can perform pulse compression of the second harmonic chirp component, with a 14% reduction in the MLW of the compressed signal when compared with the HMF. Also, the FrFT provides at least 23% reduction in the MLW of the compressed signal when compared with the harmonic mismatched filter (HMMF). The FrFT maintains comparable peak and integrated sidelobe levels when compared with the HMF and HMMF techniques.