Journal Article10.1109/LSP.2016.2633486
Closed-Form Orthogonal Ramanujan Integer Basis
Soo-Chang Pei,Kuo-Wei Chang +1 more
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TL;DR: In this letter, a closed-form orthogonal Ramanujan integer basis is proposed and obtained by performing Gram-Schmidt process from theRamanujan sum and its circular shift, which has a surprisingly simple and sparse form, which is better than the original complete Ramanuj basis.
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Abstract: In this letter, a closed-form orthogonal Ramanujan integer basis is proposed and obtained by performing Gram–Schmidt process from the Ramanujan sum and its circular shift. It has a surprisingly simple and sparse form, which is better than the original complete Ramanujan basis. The relationship between the original basis and proposed basis is also clearly illustrated. Therefore, the original basis can be replaced easily.
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References
An Introduction To The Theory Of Numbers
G. H. Hardy,Ernest M. Wright +1 more
- 31 Jul 2008
TL;DR: An Introduction to the Theory of Numbers is a classic text in elementary number theory covering key milestones and developments in the field. It is highly suitable for undergraduates and number theorists alike.
2.3K
Ramanujan Sums in the Context of Signal Processing—Part I: Fundamentals
TL;DR: In the companion paper (Part II), it is shown that arbitrary finite duration signals can be decomposed into a finite sum of orthogonal projections onto Ramanujan subspaces.
153
Ramanujan Sums in the Context of Signal Processing—Part II: FIR Representations and Applications
TL;DR: The traditional way to solve for the expansion coefficients in the Ramanujan-sum expansion does not work in the FIR case, and theRamanujan Periodic Transform (RPT) is defined based on this, and is useful to identify hidden periodicities.
129
Ramanujan sums for signal processing of low frequency noise
Michel Planat
- 16 Dec 2002
TL;DR: This work introduces a new signal processing tool based on the Ramanujan SUMS c/sub q/(n), well adapted to the analysis of arithmetical sequences with many resonances p/q, and new results arise from the use of thisRamanujan-Fourier transform (RFT).
Ramanujan sums and discrete Fourier transforms
TL;DR: A special class of even-symmetric periodic signals is introduced that their real-valued Fourier coefficients can be calculated by forming a weighted average of the signal values using integer-valued coefficients.
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