Theoretical Study On The Ramamujan Fourier Transform

With the development of signal processing technology,more and more transform domain based methods are proposed.The main difference of these transforms are the basis function.In this paper,the concept of Ramanujan Fourier transform(RFT)is introduced.The basis function of RFT is the Ramanujan Sums(RS)which are orthogonal and offer excellent energy conservation.The main content of this paper is followed as:1.Some property of the transform is shown in this paper such as linearity.The concept of Ramanujan spectrum and the spectrum estimation based on matrix-RFT is also introduced.The proposed spectrum is then used in frequency estimation,the performance of BPSK signal is better.2.The short time Ramanujan Fourier transform(ST-RFT)is proposed for signal analysis,the definition formula of ST-RFT is given,a proper transformation length of ST-RFT window width is given based on our investigation.The simulate results show the proposed transform has a good representation of the modulated signal.The formula of ST-RFT of some modulated signal are derived.The reconstitution condition and reconstitution formula is also given.3.A novel demodulation method based on ST-RFT is then introduced.It expands the received signal in a time-frequency plane via ST-RFT,the demodulation of frequency is made by searching the instantaneous spectral peaks and the demodulation of phase is made by computing the instantaneous spectral peaks amplitude.