Doppler Spectrum Estimation by Ramanujan Fourier Transforms

TL;DR

This paper introduces a novel application of Ramanujan Fourier Transforms for estimating the Doppler spectrum in weather radar signals, offering an alternative to traditional autocorrelation and Fourier-based methods.

Contribution

It presents a new signal processing tool using Ramanujan sums for Doppler spectrum estimation, enhancing analysis of arithmetical sequences with multiple resonances.

Findings

Ramanujan Fourier Transform effectively estimates Doppler spectrum.

The method captures resonances in weather radar signals.

Potential improvements over classical spectral estimation techniques.

Abstract

The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing based on Ramanujan sums cq(n), adapted to the analysis of arithmetical sequences with several resonances p/q. These sums are almost periodic according to time n of resonances and aperiodic according to the order q of resonances. New results will be supplied by the use of Ramanujan Fourier Transform (RFT) for the estimation of the Doppler spectrum for the weather radar signal.