Login | Register

Matrix-Based Ramanujan-Sums Transforms


Matrix-Based Ramanujan-Sums Transforms

Chen, Guangyi, Krishnan, Sridhar and Bui, Tien D. (2013) Matrix-Based Ramanujan-Sums Transforms. IEEE Signal Processing Letters, 20 (10). pp. 941-944. ISSN 1070-9908

Text (application/pdf)
bui2013.pdf - Accepted Version

Official URL: http://dx.doi.org/10.1109/LSP.2013.2273973


In this letter, we study the Ramanujan Sums (RS) transform by means of matrix multiplication. The RS are orthogonal in nature and therefore offer excellent energy conservation capability. The 1-D and 2-D forward RS transforms are easy to calculate, but their inverse transforms are not defined in the literature for non-even function $ ({rm mod}~ {rm M}) $. We solved this problem by using matrix multiplication in this letter.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Computer Science and Software Engineering
Item Type:Article
Authors:Chen, Guangyi and Krishnan, Sridhar and Bui, Tien D.
Journal or Publication:IEEE Signal Processing Letters
Digital Object Identifier (DOI):10.1109/LSP.2013.2273973
Keywords:Fourier transform (FT) Gaussian white noise Ramanujan Sums (RS)
ID Code:977893
Deposited On:01 Oct 2013 19:39
Last Modified:18 Jan 2018 17:45


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
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Back to top Back to top