Extended Gaussian Filtering for Noise Reduction in Spectral Analysis
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Extended Gaussian Filtering for Noise Reduction in Spectral Analysis V. L. Le∗ Department of Physics, Kyung Hee University, Seoul 02447, Korea and Laboratory of Plasma Technology, Institute of Materials Science, Vietnam Academy of Science and Technology, Hanoi 100000, Vietnam
T. J. Kim∗ Department of Physics, Kyung Hee University, Seoul 02447, Korea and Center for Converging Humanities, Kyung Hee University, Seoul 02447, Korea
Y. D. Kim† Department of Physics, Kyung Hee University, Seoul 02447, Korea
D. E. Aspnes‡ Department of Physics, North Carolina State University, Raleigh, NC 27695-8202, USA (Received 14 November 2019; revised 9 December 2019; accepted 10 December 2019) We present a method of reducing noise in spectra that is based on eliminating low-order derivatives of reciprocal-space (RS) filter functions, yet ensuring that the functions roll off smoothly to minimize Gibbs oscillations. The approach takes advantage of the fact that information and noise are separated in RS. The method preserves as much information as possible, while reducing or even eliminating unwanted contributions (noise). To demonstrate the method we apply it to a model spectrum, data including an XPS spectrum of S2p in hierarchical NiCo2 S4 nanosheets, and the Raman spectrum of 10-layer film of FePS3 with polarization direction of 90◦ with respect to the a-axis. Keywords: Reducing noise, Information, Reciprocal-space DOI: 10.3938/jkps.77.819
I. INTRODUCTION Extracting information from spectra, obtained by optical or other methods, is a fundamental goal of spectroscopy. Information can take the form of exact, noisefree shapes of spectra, or the poles of the Green function that give rise to features in these spectra. These poles are solutions of the homogeneous equation, called critical points in older literature [1] and plasmons [2] in current terminology. While most data fortunately do not require additional processing, marginal structures often exist, whose properties can be determined only by enhancing sensitivity and/or reducing noise. We consider noise reduction here. A common approach is direct-space (DS) convolution, where the data are convolved with a small set of coefficients [3–8] that achieve a specific objective, such as smoothing or smoothing combined with differentiation. ∗ These
authors contributed equally to this work. [email protected] ‡ E-mail: [email protected] † E-mail:
pISSN:0374-4884/eISSN:1976-8524
A disadvantage of the DS approach is pointed out by Kaiser and Reed [9], in that filtering algorithms are usually “applied blindly to the data and the results are simply inspected to see if they ‘look good’”. Intelligent processing (filtering) of data by using this approach can only be done by considering the reciprocal-space (RS) behavior of both the data and the convolving coefficients [9– 16]. While the inspection of the Fourier-domain behavior may appear to be an unnecessary complication to those doing DS convolutions, the conclusion follows because the Fourier transform (FT) of a convolution of two functions is equal to th
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