A New Implementation of the Mellin Transform and its Application to Radar Classification of Ships

TLDR: A modified Mellin transform for digital implementation is developed and applied to range radar profiles of naval vessels and results in the desired insensitivity without having the low-pass filtering characteristic that exists in other Fourier-Mellin implementations.

Abstract: A modified Mellin transform for digital implementation is developed and applied to range radar profiles of naval vessels. The scale invariance property of the Mellin transform provides a means for extracting features from the profiles which are insensitive to the aspect angle of the radar. Past implementations of the Mellin transform based on the FFT have required exponential sampling, interpolation, and the computation of a correction term, all of which introduce errors into the transform. In addition, exponential sampling results in a factor of ln N increase in the number of data points. An alternate implementation, developed in the paper, utilizes a direct expansion of the Mellin integral definition. This direct Mellin transform (DMT) eliminates the implementation problems associated with the FFT approach, and does not increase the number of samples. A scale and translation invariant transform is developed from a modification of the DMT. The MDMT applied to the FFT of the radar profiles results in the desired insensitivity without having the low-pass filtering characteristic that exists in other Fourier-Mellin implementations.