Applying the Fourier-modified Mellin transform (FMMT) to Doppler-distorted waveforms

The magnitude spectrum of a time domain signal has the property of delay-invariance. Similar to the delay-invariance property of the Fourier transform, the Mellin transform has the property of scale-invariance. By combining these two transforms together one can form the Fourier-Mellin transform that yields a signal representation which is independent of both delay and scale change. Due to the undesired low-pass property of the Mellin transform (MT), the modified Mellin transform (MMT) which is also scale-invariant is applied in our approach. Therefore the Fourier-modified Mellin transform (FMMT) of the original signal and the Doppler-distorted signal will be identical. This signal representation is useful in signal detection and target recognition. Several examples dealing with different waveforms have been simulated to illustrate the applicability of this approach. The performance of the Fourier-modified Mellin transform under different levels of noise in the signal are also illustrated in this paper.