Doppler spectrum estimation by Ramanujan-Fourier Transform (RFT)

Lagha, Mohand; Bensebti, Messaoud

doi:10.1016/j.dsp.2009.03.007

Cited by 18 publications

(11 citation statements)

References 12 publications

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“…However, the peculiarity of AD-plane is that, in this domain the signal terms appear localized around the origin and the cross-terms are located away from the origin [14]. In this work, a modified AF representation is computed by using the RS (on the time-varying autocorrelation values) as (8) Such a computation results in an overall reduction in the number of AD coefficients. These AD-mapped coefficients can then be transformed into a sparser time-frequency representation, using the RFT computed from their characteristic RS.…”

Section: B Rationalementioning

confidence: 98%

“…Their research showed that in the presence of Gaussian noise, RFT captures the signal periodicities better than the conventional DFT. Lagha et al [8] expanded on the theory of usability of this transform for estimation of Doppler spectral parameters for weather signals. The usefulness of this class of transform is also reported for analysis of biomedical signals, such as T-wave alternans, by Mainardi et al [9].…”

Section: Introductionmentioning

confidence: 99%

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Time-Frequency Analysis via Ramanujan Sums

Sugavaneswaran

Xie

Umapathy

et al. 2012

IEEE Signal Process. Lett.

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Research in signal processing shows that a variety of transforms have been introduced to map the data from the original space into the feature space, in order to efficiently analyze a signal. These techniques differ in their basis functions, that is used for projecting the signal into a higher dimensional space. One of the widely used schemes for quasi-stationary and non-stationary signals is the time-frequency (TF) transforms, characterized by specific kernel functions. This work introduces a novel class of Ramanujan Fourier Transform (RFT) based TF transform functions, constituted by Ramanujan sums (RS) basis. The proposed special class of transforms offer high immunity to noise interference, since the computation is carried out only on co-resonant components, during analysis of signals. Further, we also provide a 2-D formulation of the RFT function. Experimental validation using synthetic examples, indicates that this technique shows potential for obtaining relatively sparse TF-equivalent representation and can be optimized for characterization of certain real-life signals.

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Section: B Rationalementioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Time-Frequency Analysis via Ramanujan Sums

Sugavaneswaran

Xie

Umapathy

et al. 2012

IEEE Signal Process. Lett.

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“…These base functions satisfy many suitable properties for signal decomposition such as multiplicative and orthogonality properties. Alternatively, the Ramanujan sums can be evaluated using the Euler totient function φ(q) and Moebius function µ(n) as follows (Lagha and Bensebti, 2009)…”

Section: Ramanujan-fourier Transformmentioning

confidence: 99%

A Novel Method for Comparative Analysis of DNA Sequences by Ramanujan-Fourier Transform

Yin

Yin²,

Wang

2014

Journal of Computational Biology

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Alignment-free sequence analysis approaches provide important alternatives over multiple sequence alignment (MSA) in biological sequence analysis because alignment-free approaches have low computation complexity and are not dependent on high level of sequence identity, however, most of the existing alignment-free methods do not employ true full information content of sequences and thus can not accurately reveal similarities and differences among DNA sequences. We present a novel alignment-free computational method for sequence analysis based on Ramanujan-Fourier transform (RFT), in which complete information of DNA sequences is retained. We represent DNA sequences as four binary indicator sequences and apply RFT on the indicator sequences to convert them into frequency domain. The Euclidean distance of the complete RFT coefficients of DNA sequences are used as similarity measure. To address the different lengths in Euclidean space of RFT coefficients, we pad zeros to short DNA binary sequences so that the binary sequences equal the longest length in the comparison sequence data. Thus, the DNA sequences are compared in the same dimensional frequency space without information loss. We demonstrate the usefulness of the proposed method by presenting experimental results on hierarchical clustering of genes and genomes. The proposed method opens a new channel to biological sequence analysis, classification, and structural module identification.

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“…The shape of the received signal reflected by all particles met by the transmitted beam is: [3], [5], [8].…”

Section: Estimation Theorymentioning

confidence: 99%

Performances comparison of pulse pair and wavelets methods for the pulse Doppler weather radar spectrum

Lagha¹,

Tikhemirine²,

Bergheul³

et al. 2010

SPIE Proceedings

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In the civilian aviation field, the radar detection of hazardous weather phenomena (winds) is very important. This detection will allow the avoidance of these phenomena and consequently will enhance the safety of flights. In this work, we have used the wavelets method to estimate the mean velocity of winds. The results showed that the application of this method is promising compared with the classical estimators (pulse pair, Fourier).

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Doppler spectrum estimation by Ramanujan-Fourier Transform (RFT)

Cited by 18 publications

References 12 publications

Time-Frequency Analysis via Ramanujan Sums

Time-Frequency Analysis via Ramanujan Sums

A Novel Method for Comparative Analysis of DNA Sequences by Ramanujan-Fourier Transform

Performances comparison of pulse pair and wavelets methods for the pulse Doppler weather radar spectrum

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