Adaptive fractional Fourier domain filtering

Durak, Lütfiye; Aldırmaz, Sultan

doi:10.1016/j.sigpro.2009.10.002

Cited by 35 publications

(13 citation statements)

References 23 publications

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“…This performance of LEF signals is different from those presented with chirp and LFM signals where the adaptation of algorithm is presented at the initial stage of the FRFT signal and the fast adaptation of the filter reduces gradually the error [29].…”

Section: Performance Analysis and Complexity Of Adaptive Algorithmsmentioning

confidence: 75%

“…[28][29][30] show that these algorithms present good results with LFM signals because FRFT converts this type of signals into stationary sinusoidal signals at the appropriate transformation order. However, with transient signals (as lightning electromagnetic fields), the FRFT converts a LEF signal into a narrow band signal with a symmetric center u 0 .…”

Section: Fractional Order Estimation For Lef Signalsmentioning

confidence: 99%

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Denoising of measured lightning electric field signals using adaptive filters in the fractional Fourier domain

Rojas

Cortés

2014

Measurement

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Section: Performance Analysis and Complexity Of Adaptive Algorithmsmentioning

confidence: 75%

Section: Fractional Order Estimation For Lef Signalsmentioning

confidence: 99%

Denoising of measured lightning electric field signals using adaptive filters in the fractional Fourier domain

Rojas

Cortés

2014

Measurement

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“…It is hard to obtain a satisfactory analysis for this kind of multi-component signal using existing methods. The fractional Fourier transform [14][15][16] can be used to analyze multi-component LFM signals only, and the estimated frequency obtained by using the energy operator [17] has large error margins. A possible alternative is time-frequency analysis [11][12][13], but the cross terms in the time-frequency distribution would greatly impact the effect, as is shown in Fig.…”

Section: Simulation and Analysismentioning

confidence: 99%

“…19, we give the estimation precision (NRMSE curves) of all the parameters under different sampling frequencies (F s = k × Fn, k = 1 · · · 8, Fn = 38.4 MHz, 2Fn = 76.8 MHz is the sampling frequency of the signals corresponding to Figs. [10][11][12][13][14][15][16][17][18] and SNRs, and we see that the NRMSE is lower when the sampling frequency is higher.…”

Section: Simulation and Analysismentioning

confidence: 99%

Single channel source separation and parameter estimation of multi-component PRBCPM-SFM signal based on generalized period

Zhu

Zhang

Zhao

2015

Digital Signal Processing

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“…In particular, the optimum multiplicative filter function that minimizes the mean square error in the αth fractional Fourier domain was derived in [80]. Similarly, a novel fractional adaptive filtering scheme was introduced [81], and simulation results showed that adaptive filtering in the fractional domain is superior in comparison to its time domain counterparts.…”

Section: A Filteringmentioning

confidence: 99%

Fractional Fourier transform as a signal processing tool: An overview of recent developments

2011

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-Fractional Fourier transform (FRFT) is a generalization of the Fourier transform, rediscovered many times over the past hundred years. In this paper, we provide an overview of recent contributions pertaining to the FRFT. Specifically, the paper is geared toward signal processing practitioners by emphasizing the practical digital realizations and applications of the FRFT. It discusses three major topics. First, the manuscripts relates the FRFT to other mathematical transforms. Second, it discusses various approaches for practical realizations of the FRFT. Third, we overview the practical applications of the FRFT. From these discussions, we can clearly state the FRFT is closely related to other mathematical transforms, such as time-frequency and linear canonical transforms. Nevertheless, we still feel that major contributions are expected in the field of the its digital realizations and applications, especially, since many digital realizations of the FRFT still lack properties of the continuous FRFT. Overall, the FRFT is a valuable signal processing tool. Its practical applications are expected to grow significantly in years to come, given that the FRFT offers many advantages over the traditional Fourier analysis. I. IIn very simple terms, the fractional Fourier transform (FRFT) is a generalization of the ordinary Fourier transform [1]. Specifically, the FRFT implements the so-called order parameter α which acts on the ordinary Fourier transform operator. In other words, the αth order fractional Fourier transform represents the αth power of the ordinary Fourier transform operator. When α = π/2, we obtain the Fourier transform, while for α = 0, we obtain the signal itself. Any intermediate value of α (0 < α < π/2) produces a signal representation that can be considered as a rotated time-frequency representation of the signal [2], Signal Processing, Vol. 91 No. 6, June, 2011 [3].Interestingly enough, the idea of the fractional powers of the Fourier operator has been "discovered" several times in the literature. Initially, the idea appeared in the mathematical literature between the two world wars (e.g., [4], [5]). More publications relating to this idea appeared after the second world war, however they were sporadic (e.g. [6]). The idea of fractional Fourier operator re-gains a momentum in 1980's with publications by Namias (e.g. [7]). Following Namias' contributions, a large number of papers appeared in the literature during 1990's tying the concept of the fractional Fourier operators to many other fields (e.g., time-frequency analysis as described in [2]). We have also witnessed a number of recent contributions attempting to understand the practical applications of the FRFT beyond optics.The main goal of this publication is to provide an overview of recent developments regarding the FRFT and its applications. Although a number of publications reviewing the FRFT has also appeared in recent years (e.g., [1], [8], [9]), some of these publications are geared towards explaining the mathematical eloquence b...

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Adaptive fractional Fourier domain filtering

Cited by 35 publications

References 23 publications

Denoising of measured lightning electric field signals using adaptive filters in the fractional Fourier domain

Denoising of measured lightning electric field signals using adaptive filters in the fractional Fourier domain

Single channel source separation and parameter estimation of multi-component PRBCPM-SFM signal based on generalized period

Fractional Fourier transform as a signal processing tool: An overview of recent developments

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