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A classic application of the Mellin transform is in radar engineering. Recall that the resolution in time of a signal is the reciprocal of the spread of its Fourier transform. In radar (or sonar) a signal is reflected from a moving target and you would like to accurately determine its velocity. The velocity resolution of the signal is the reciprocal of the spread of its Mellin transform.

Cramer Rao bound computation for velocity estimation in the broad-band case using the Mellin transform