Ramanujan sums for signal processing of low-frequency noise

Planat, Michel; Rosu, H. C.; Perrine, Serge

doi:10.1103/physreve.66.056128

Cited by 35 publications

(25 citation statements)

References 13 publications

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“…In physics, Ramanujan sums have applications in the processing of low-frequency noise [49] and of long-period sequences [48] and in the study of quantum phase locking [50]. We should also remark that various generalizations of the classical Ramanujan sum (1.1) have arisen over the years [2,11,12,58] and that Ramanujan sums involving matrix variables have also been considered [45,52].…”

Section: Ramanujan Sumsmentioning

confidence: 99%

Ramanujan sums as supercharacters

2013

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Abstract. The theory of supercharacters, recently developed by DiaconisIsaacs and André, can be used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and provides many novel formulas. In addition to exhibiting a new application of supercharacter theory, this article also serves as a blueprint for future work since some of the abstract results we develop are applicable in much greater generality. IntroductionOur primary aim in this note is to demonstrate that most of the fundamental algebraic properties of Ramanujan sums can be deduced using the theory of supercharacters, recently developed by Diaconis-Isaacs and André. In fact, the machinery of supercharacter theory frequently yields one-line proofs of many difficult identities and provides an array of new tools which can be used to derive various novel formulas. Our approach is entirely systematic, relying on a flexible and general framework. Indeed, we hope to convince the reader that supercharacter theory provides a natural framework for the study of Ramanujan sums. In addition to exhibiting a novel application of supercharacter theory, this article also serves as a blueprint for future work since some of the abstract results which we develop are applicable in much greater generality (see [10]). Ramanujan sums.In what follows, we let e(x) = exp(2πix), so that the function e(x) is periodic with period 1. For integers n, x with n ≥ 1, the expression

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Section: Ramanujan Sumsmentioning

confidence: 99%

Ramanujan sums as supercharacters

2013

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“…The use of the Ramanujan method in the domain of the Doppler spectrum estimation of the weather radar signals, has been motivated by the recent researchers' growing interest to introduce it as a new tool in signal processing [9] [10]. This method has been used by Ramanujan, for the first time, as a means for representing arithmetic series by infinite extent sums.…”

Section: Introductionmentioning

confidence: 99%

Doppler spectrum estimation by Ramanujan-Fourier Transform (RFT)

Lagha¹,

Bensebti²

2009

Digital Signal Processing

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Abstract.The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing based on Ramanujan sums cq(n), adapted to the analysis of arithmetical sequences with several resonances p/q. These sums are almost periodic according to time n of resonances and aperiodic according to the order q of resonances. New results will be supplied by the use of Ramanujan Fourier Transform (RFT) for the estimation of the Doppler spectrum for the weather radar signal.

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“…Recently, the concept of Ramanujan Fourier Transform(RFT) based time-frequency transform, namely Short-time Ramanujan Fourier transform(ST-RFT) has been investigated owing to the good immunity to noise interference of RFT functions [16][17][18]. Following this, the time-frequency analysis of signals based on RFT was considered in a letter by Sugavaneswaran [19].…”

Section: Introductionmentioning

confidence: 99%

Intra-pulse modulation recognition using short-time ramanujan Fourier transform spectrogram

Liu

Shan

2017

EURASIP J. Adv. Signal Process.

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Intra-pulse modulation recognition under negative signal-to-noise ratio (SNR) environment is a research challenge. This article presents a robust algorithm for the recognition of 5 types of radar signals with large variation range in the signal parameters in low SNR using the combination of the Short-time Ramanujan Fourier transform (ST-RFT) and pseudo-Zernike moments invariant features. The ST-RFT provides the time-frequency distribution features for 5 modulations. The pseudo-Zernike moments provide invariance properties that are able to recognize different modulation schemes on different parameter variation conditions from the ST-RFT spectrograms. Simulation results demonstrate that the proposed algorithm achieves the probability of successful recognition (PSR) of over 90% when SNR is above -5 dB with large variation range in the signal parameters: carrier frequency (CF) for all considered signals, hop size (HS) for frequency shift keying (FSK) signals, and the time-bandwidth product for Linear Frequency Modulation (LFM) signals.

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Ramanujan sums for signal processing of low-frequency noise

Cited by 35 publications

References 13 publications

Ramanujan sums as supercharacters

Ramanujan sums as supercharacters

Doppler spectrum estimation by Ramanujan-Fourier Transform (RFT)

Intra-pulse modulation recognition using short-time ramanujan Fourier transform spectrogram

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