In this paper, the detection of shock wave that generated by supersonic bullet is considered. We present a new framework based on wavelet multi-scale products method. We analyze the method under the standard likelihood ratio test. It is found that the multi-scale product method is made in an assumption that is extremely restricted, just hold for a special noise condition. Based on the analysis, a general condition is considered for the detection. An optimal detector under the standard likelihood ratio test is proposed. Monte Carlo simulations is conducted with simulated shock waves under additive white Gaussian noise. The result shows that this new detection algorithm outperforms the conventional detection algorithm.

The URL for my published paper in IEEE Xplore is http://dx.doi.org/10.1109/ChinaSIP.2015.7230361.