Ramanujan sums （RS） and their Fourier transforms have attracted more and more attention in signal processing in recent years. Due to their non-periodic and non-uniform spectrum, RS are widely used in low-frequency n...Ramanujan sums （RS） and their Fourier transforms have attracted more and more attention in signal processing in recent years. Due to their non-periodic and non-uniform spectrum, RS are widely used in low-frequency noise processing, Doppler spectrum estimation and time-frequency analysis. However, the traditional method for calculating RS values is rather complex since it requires two numbers＇ factorization in two arithmetic functions. For a length-n vector, its Ramanujan-Fourier transform usually involves a series of RS values which will occupy O（n2） memory units. Thus, in this paper an approach based on prime-composition is proposed to reduce the complexity of RS calculation to O（n）. Meanwhile, the complexity of Ramanujan-Fourier transform can be further reduced from O（n2） to O（n In（In（n））） .展开更多
基金Supported by the National Natural Science Foundation of China(No.61071070)
文摘Ramanujan sums （RS） and their Fourier transforms have attracted more and more attention in signal processing in recent years. Due to their non-periodic and non-uniform spectrum, RS are widely used in low-frequency noise processing, Doppler spectrum estimation and time-frequency analysis. However, the traditional method for calculating RS values is rather complex since it requires two numbers＇ factorization in two arithmetic functions. For a length-n vector, its Ramanujan-Fourier transform usually involves a series of RS values which will occupy O（n2） memory units. Thus, in this paper an approach based on prime-composition is proposed to reduce the complexity of RS calculation to O（n）. Meanwhile, the complexity of Ramanujan-Fourier transform can be further reduced from O（n2） to O（n In（In（n））） .
