The theoretical prediction, interpretation and computation of the Fourier-Mellin transform applied to sonar classification of ships

The Fourier-Mellin transforms of sonar target returns for linear frequency-modulated and linear period-modulated pulse transmission cases are obtained analytically by modeling a target as a collection of discrete reflectors located randomly over the length of the target. Simulation studies have been performed. It is shown that the synthesized Fourier-Mellin transforms converge to the theoretical prediction as the number of points in the Fourier transform of the matched filter output (input to the direct Mellin transform) over the range [0,W] increases, where W is the bandwidth of the transmitted pulse