Recursive sliding DFT algorithms: A review

Chauhan, Abhishek; Singh, Ksh. Milan

doi:10.1016/j.dsp.2022.103560

Cited by 19 publications

(4 citation statements)

References 52 publications

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“…During the testing period, we employ the sliding discrete Fourier transform (SDFT) [45,58,59] to recursively update the temporal Fourier coefficients of the measurements at every time step, 𝑡 𝑖 . We thereby enable efficient updates of our triplet space measurements as new data arrives.…”

Section: Recursive Sliding Discrete Fourier Transformmentioning

confidence: 99%

“…The standard SDFT algorithm suffers from marginal stability, moderate accuracy, and time-accumulating error (such that, eventually, the fft algorithm would need to be called to refresh the error). The more recent modulated SDFT (mSDFT) [58] and observer-based SDFT (oSDFT) [59] have more desirable stability, accuracy, and robustness to noise compared to the standard SDFT and other variants [45]. However, we retain the standard SDFT due to its simple implementation and since it remains accurate and stable over sufficiently large intervals for our purposes (see Appendix B).…”

Section: Recursive Sliding Discrete Fourier Transformmentioning

confidence: 99%

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Towards Real-Time Reconstruction of Velocity Fluctuations in Turbulent Channel Flow

Arun¹,

Bae²,

McKeon³

2023

Preprint

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We develop a framework for efficient streaming reconstructions of turbulent velocity fluctuations from limited sensor measurements with the goal of enabling real-time applications. The reconstruction process is simplified by computing linear estimators using flow statistics from an initial training period and evaluating their performance during a subsequent testing period with data obtained from direct numerical simulation (DNS). We address cases where (i) no, (ii) limited, and (iii) full-field training data are available using estimators based on (i) resolvent modes, (ii) resolvent-based estimation, and (iii) spectral proper orthogonal decomposition modes. During training, we introduce blockwise inversion to accurately and efficiently compute the resolvent operator in an interpretable manner. During testing, we enable efficient streaming reconstructions by using a temporal sliding discrete Fourier transform to recursively update Fourier coefficients using incoming measurements. We use this framework to reconstruct with minimal time delay the turbulent velocity fluctuations in a minimal channel at 𝑅𝑒 𝜏 ≈ 186 from sparse planar measurements. We evaluate reconstruction accuracy in the context of the extent of data required and thereby identify potential use cases for each estimator. The reconstructions capture large portions of the dynamics from relatively few measurement planes when the linear estimators are computed with sufficient fidelity. We also evaluate the efficiency of our reconstructions and show that the present framework has the potential to enable real-time reconstructions of turbulent velocity fluctuations in an analogous experimental setting.

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Section: Recursive Sliding Discrete Fourier Transformmentioning

confidence: 99%

Section: Recursive Sliding Discrete Fourier Transformmentioning

confidence: 99%

Towards Real-Time Reconstruction of Velocity Fluctuations in Turbulent Channel Flow

Arun¹,

Bae²,

McKeon³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In particular, as a novelty, the observer's ability to reconstruct noncoherent signals was proven which to the best knowledge of the authors has not been done before in this general setting. The main area of application of the observer is the recursive implementation of the DFT [6] [7] [8] and in that special case a modified observer structure can be used which is time invariant so the analysis is different.…”

Section: Expression Of State Estimation Errormentioning

confidence: 99%

Behavior of Observer Performing Discrete Gabor Transform

Ország¹,

Sujbert²

2023

Proceedings of the 30th Minisymposium

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The theory of discrete Gabor transforms provides a constructive and interpretable way of creating biorthogonal transforms. These transforms can achieve a non-uniform frequency resolution and they can be implemented recursively by observers based on Hostetter's approach. The dead-beat property of the observers were previously shown for coherent signals with the help of an adequately chosen conceptual signal model. This paper investigates the properties of the signal modelobserver pair and derives the dead-beat property in the case of noncoherent signals based on a modified signal model.

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“…Theoretical chemical calculations have proven crucial in elucidating the molecule's architectures, properties, processes, and reaction selectivity. The most common theoretical approaches used to calculate various molecular properties include DFT (density functional theory), optimized molecular structures, vibrational frequencies, and chemical shifts [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Computational Investigation of 5.5'',7''-trihydroxy-3,7-dimethoxy-4'-4''-O-biflavone from Flavonoids Using DFT Calculations and Molecular Docking

2022

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The structural characterization of the 5.5",7"-trihydroxy-3,7-dimethoxy-4'-4"-O-biflavone (TDOB) molecule was done in this study. Based on the molecule's stable phase geometry, entire calculations were done by use of the detailed CAM-B3LYP and PBEPBE approach with SDD and LanL2DZ. In addition, a variety of HOMO-LUMO energy ranges, natural bond inter-orbital and inter-orbital interactions, and electro-static surface mapping operations were as well carried out. The specific binding location and mechanism of the ligand on the protein were studied using molecular docking. In the study, affinity scores for TDOB-AKR1B1 (Aldose Reductase) (PDB: 4ICC) and (PDB: 4IGS) were found to be -8.559 cal/mol and -5.461 cal/mol, respectively. 4ICC receptor binding score was found to be greater. The inhibitory properties of TDOB were investigated against the enzymes 4ICC and 4IGS, both of which showed effective inhibition.

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Recursive sliding DFT algorithms: A review

Cited by 19 publications

References 52 publications

Towards Real-Time Reconstruction of Velocity Fluctuations in Turbulent Channel Flow

Towards Real-Time Reconstruction of Velocity Fluctuations in Turbulent Channel Flow

Behavior of Observer Performing Discrete Gabor Transform

Computational Investigation of 5.5'',7''-trihydroxy-3,7-dimethoxy-4'-4''-O-biflavone from Flavonoids Using DFT Calculations and Molecular Docking

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