Spectral Correlation Density Estimation Using 2N-FFT Interpolation

Shevgunov, Timofey

doi:10.1109/emctech53459.2021.9619185

Cited by 6 publications

(2 citation statements)

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“…In spite of the fact that there exist SCF estimators performing in wide frequency ranges, we suppose that there is still room for yet another estimator if it is able to show a sufficient computational effectiveness while minimizing the drawbacks, such as the degradation of the resolution of the cells or an uneven grid of the nodes in the bifrequency plane where the estimates are evaluated. Although this algorithm was developed by the authors as early as in 2014, it remained unavailable for a wider community for several years, until it was reported at conference© 2021 IEEE [ 43 ]. Since the format of that conference paper did not let to provide all the details of the method, the current paper is aimed at eliminating this gap by giving a thorough description of the algorithm, accompanied by graphical illustrations explaining some of its essential operations.…”

Section: Introductionmentioning

confidence: 99%

“…Since the format of that conference paper did not let to provide all the details of the method, the current paper is aimed at eliminating this gap by giving a thorough description of the algorithm, accompanied by graphical illustrations explaining some of its essential operations. Compared to [ 43 ], this paper contains a completely new example involving a pulse-amplitude modulation (PAM) and a section containing a comparison of computational complexity between FAM and the proposed algorithm. All simulation examples are now provided with all necessary spectral and cyclic sample characteristics.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of a Spectral Correlation Function Using a Time-Smoothing Cyclic Periodogram and FFT Interpolation—2N-FFT Algorithm

Shevgunov

Efimov

Guschina

2022

Sensors

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This article addresses the problem of estimating the spectral correlation function (SCF), which provides quantitative characterization in the frequency domain of wide-sense cyclostationary properties of random processes which are considered to be the theoretical models of observed time series or discrete-time signals. The theoretical framework behind the SCF estimation is briefly reviewed so that an important difference between the width of the resolution cell in bifrequency plane and the step between the centers of neighboring cells is highlighted. The outline of the proposed double-number fast Fourier transform algorithm (2N-FFT) is described in the paper as a sequence of steps directly leading to a digital signal processing technique. The 2N-FFT algorithm is derived from the time-smoothing approach to cyclic periodogram estimation where the spectral interpolation based on doubling the FFT base is employed. This guarantees that no cyclic frequency is left out of the coverage grid so that at least one resolution element intersects it. A numerical simulation involving two processes, a harmonic amplitude modulated by stationary noise and a binary-pulse amplitude-modulated train, demonstrated that their cyclic frequencies are estimated with a high accuracy, reaching the size of step between resolution cells. In addition, the SCF components estimated by the proposed algorithm are shown to be similar to the curves provided by the theoretical models of the observed processes. The comparison between the proposed algorithm and the well-known FFT accumulation method in terms of computational complexity and required memory size reveals the cases where the 2N-FFT algorithm offers a reasonable trade-off.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%