1. S. Ramanujan  "On certain trigonometric sums and their applications",  Trans. Cambridge Philos. Soc.,  vol. 22,  pp.259 -276 1918 

2. L. Sugavaneswaran , S. Xie , K. Umapathy and S. Krishnan  "Time-frequency analysis via Ramanujan sums",  IEEE Signal Process. Lett.,  vol. 19,  no. 6,  pp.352 -355 2012 

3. M. Planat  "Ramanujan sums for signal processing of low frequency noise",  Phys. Rev. E.,  vol. 66,  2002 
 
4. S. Samadi , M. O. Ahmad and M. N. S. Swamy  "Ramanujan sums and discrete Fourier transform",  IEEE Signal Process. Lett.,  vol. 12,  no. 4,  pp.293 -296 2005 

5. L. T. Mainardi , L. Pattini and S. Cerutti  "Application of the Ramanujan Fourier transform for the analysis of secondary structure content in amino acid sequences",  Meth. Inf. Med.,  vol. 46,  no. 2,  pp.126 -129 2007 

6. L. T. Mainardi , M. Bertinelli and R. Sassi  "Analysis of T-wave alternans using the Ramanujan Sums",  Comput. Cardiol.,  vol. 35,  pp.605 -608 2008 

7. G. Y. Chen , S. Krishnan and T. D. Bui  "Ramanujan sums for image pattern analysis",  Int. J. Wavelets, Multires. Inf. Process.,  

8. G. Y. Chen , S. Krishnan , W. Liu and W. F. Xie  "Ramanujan sums for sparse signal analysis",  Proc. Ninth Int. Conf. Intelligent Computing (ICIC),  2013 
 
9. G. Y. Chen , S. Krishnan and W. F. Xie  "Ramanujan Sums-wavelet transform for signal analysis",  Proc. Int. Conf. on Wavelet Anal. and Pattern Recognition (ICWAPR),  2013 

10. P. Haukkanen  "Discrete Ramanujan-Fourier transform of even functions $ ({\rm mod}~{\rm r}) $",  Indian J. Math. Math. Sci.,  vol. 3,  no. 1,  pp.75 -80 2007 

11. T. M. Apostol  "Arithmetical properties of generalized Ramanujan sums",  Pacific J. of Mathematics,  vol. 41,  no. 2,  1972 

12. I. Korkee and P. Haukkanen  "On a general form of meet matrices associated with incidence functions",  Linear and Multilinear Algebra,  vol. 53,  no. 5,  pp.309 -321 2005 

13. P. J. McCarthy  "A generalization of Smith\'s determinant",  Canad. Math. Bull.,  vol. 29,  no. 1,  pp.109 -113 1986