Simplified ZoomFFT algorithm in digital sonar

DEMON and LOFAR have been proved the powerful mean in underwater acoustic signal processing, especially in weak signal detection and target noise classification. Sometimes one needs to know the fine structure of frequency spectrum of received signal. It is necessary to take a very long data to get high frequency resolution. This is not always possible due to the hardware and software limitation. ZoomFFT is one of the trade-off consideration for solving high frequency resolution problem, if we are only focus on some special frequency bins. Previous discussions mainly bifurcate into two different representations, the Complex Modulation and Cascade. The former one traditionally needs some kinds of special treatment, e.g. the complex modulation, Lowpass filtering, down-sampling; while the latter achieves te same result by two successive FFT, with certain necessary modifications in phase and amplitude, thus is feasible for real-time implementation. Based on theoretical analysis, a relationship between the Complex Modulation and Cascade FFT was described. In addition, the selection of parameters such as sampling rate, overlap factor was discussed. Finally, an algorithm was presented and some simulation results were illustrated.