Abstract
Ramanujan Sums (RS) and their Fourier transforms attract many attentions in signal processing in recent years. Thanks to their non-periodic and non-uniform spectrum, RS are widely used in low-frequency noise processing, e.g., Doppler spectrum estimation and time-frequency analysis. We proved the transforms can be perfectly reconstructed under certain circumstance and built a multi-tone system using Ramanujan Fourier transforms as modulation and demodulation. This system got a lower BER in AWGN channel compare to OFDM.
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