Brian M. Sadler
Tien Pham
Army Res. Lab., Adelphi, MD 20783
Wavelets were applied to experimentally obtained acoustic time series for detection and characterization of shockwaves generated by supersonic projectiles. Exploitation of the shockwave (N wave) for detection is useful in noisy, echo-filled environments. Wavelets generated from the derivative of a quadratic spline yield a wavelet transform (WT) with a deterministic relationship between the WT modulus-maxima and sharp transitions of the signal [S. Mallat and W. Hwang, IEEE Trans. Inf. Theory 38, 617--643 (1992)]. This WT is dyadic in scale but includes all signal shifts. Shockwave detection was accomplished by analyzing across scales. Analysis proceeds from large to small scales because large scales are more low pass and thus have fewer artifacts from high-frequency interference. With a sampling rate of 250 kHz the first seven or eight scales were found to be sufficient for detection and filtering. The N-wave produces characteristic double-peak waveforms at the various scales. Cross-scale analysis searches for these waveforms with constraints on N-wave duration. Detection of the leading and trailing edge of the shockwaves was achieved with high accuracy. The algorithm was validated using data from a variety of small (rifle) and large (tank) projectiles.