Fractional Fourier transform techniques applied to active sonar

The performance of the fractional Fourier transform is studied for two different applications, as an alternative to matched filtering and as a method of producing time/frequency surfaces. The fractional Fourier transform has shown several advantages over matched filtering regarding robustness against distortion of the received signal. The matched filter is only optimal in the case of the returning echo maintaining the original properties of the emitted pulse, whereas the fractional Fourier transform is still optimal as long as the chirp rate of the original signal is unaffected. Due to the fractional Fourier transform taking advantage of the known transmitted pulse in active sonar this gives an advantage over the traditional Fourier transform for making time/frequency surfaces. Time/frequency surfaces made with the traditional spectrogram are compared to surfaces made using the short time fractional Fourier transform (STFrFT). Both of these applications are studied using real data collected at two different sea trials.