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arXiv · 2503.23493

A Kolmogorov-Zurbenko Fourier Transform Band-pass Filter Extension for Time Series Analysis

Edward Valachovic
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Abstract

This research introduces a novel extension, called the Extended Kolmogorov-Zurbenko Fourier Transform (EKZFT), to an existing class of band-pass filters first introduced by Kolmogorov and Zurbenko. Their original Kolmogorov-Zurbenko Fourier Transform (KZFT) is a useful tool in time series and spatio-temporal analysis, Fourier analysis, and related statistical analysis fields. Example uses of these filters include separating frequencies, filtering portions of the spectra, reconstructing seasonality, investigating periodic signals, and reducing noise. KZFT filters have many practical applications across a wide range of disciplines including health, social, natural, and physical sciences. KZFT filters are band-pass filters defined by three arguments: the length of the filter window; the number of iterations; and the central frequency of the band-pass filter. However, the KZFT filter is limited in design to only positive odd integer widow lengths inherited from the time series. Therefore, for any combination of the other KZFT filter arguments, there is only a relatively small, discrete, selection of possible filter window lengths in a range determined by the size of the dataset. This limits the utility of KZFT filters for many of the stated uses. The proposed EKZFT filter allows a continuous selection of filter window length arguments over the same range, offering improved control, increased functionality, and wider practical use of this band-pass filter. An example application of the EKZFT in a data simulation is provided.

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Edward Valachovic. 2025-03-30. A Kolmogorov-Zurbenko Fourier Transform Band-pass Filter Extension for Time Series Analysis. https://arxiv.org/abs/2503.23493

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