摘要: Ramanujan sums have in the past been used to represent arithmetic sequences. It is shown here that for finite duration (FIR) sequences with length N, traditional representation not suitable. Two new types of Ramanujan-sum expansions are proposed FIR case, each offering an integer basis. One these particularly suited identify periodicities sequence. This fact expresses any sequence as a sum orthogonal hidden periodicity corresponding divisor N.
sci-hub.se 参考文章(13)
Soo-Chang Pei, Kuo-Wei Chang, Odd Ramanujan Sums of Complex Roots of Unity IEEE Signal Processing Letters. ,vol. 14, pp. 20- 23 ,(2007) , 10.1109/LSP.2006.881527
S. Samadi, M.O. Ahmad, M.N.S. Swamy, Ramanujan sums and discrete Fourier transforms IEEE Signal Processing Letters. ,vol. 12, pp. 293- 296 ,(2005) , 10.1109/LSP.2005.843775
P. P. Vaidyanathan, Ramanujan Sums in the Context of Signal Processing—Part II: FIR Representations and Applications IEEE Transactions on Signal Processing. ,vol. 62, pp. 4158- 4172 ,(2014) , 10.1109/TSP.2014.2331624
P. P. Vaidyanathan, Piya Pal, The farey-dictionary for sparse representation of periodic signals international conference on acoustics, speech, and signal processing. pp. 360- 364 ,(2014) , 10.1109/ICASSP.2014.6853618
R. D. Carmichael, Expansions of Arithmetical Functions in Infinite Series Proceedings of The London Mathematical Society. pp. 1- 26 ,(1932) , 10.1112/PLMS/S2-34.1.1
Lakshmi Sugavaneswaran, Shengkun Xie, Karthikeyan Umapathy, Sridhar Krishnan, Time-Frequency Analysis via Ramanujan Sums IEEE Signal Processing Letters. ,vol. 19, pp. 352- 355 ,(2012) , 10.1109/LSP.2012.2194142
Michel Planat, Metod Saniga, Milan Minarovjech, Ramanujan sums analysis of long-period sequences and 1/f noise EPL. ,vol. 85, pp. 40005- ,(2009) , 10.1209/0295-5075/85/40005
M. Planat, Ramanujan sums for signal processing of low frequency noise international frequency control symposium. pp. 715- 720 ,(2002) , 10.1109/FREQ.2002.1075974
Chen Nan-xian, Chen Zhao-dou, Wei Yu-chuan, Multidimensional inverse lattice problem and a uniformly sampled arithmetic Fourier transform Physical Review E. ,vol. 55, pp. R5- R8 ,(1997) , 10.1103/PHYSREVE.55.R5
L.T. Mainardi, M. Bertinelli, R. Sassi, Analysis of T-wave alternans using the Ramanujan transform 2008 Computers in Cardiology. pp. 605- 608 ,(2008) , 10.1109/CIC.2008.4749114