{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T07:55:30Z","timestamp":1789718130709,"version":"4.0.1"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2013,7,19]],"date-time":"2013-07-19T00:00:00Z","timestamp":1374192000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>A novel noise filtering algorithm based on averaging Intrinsic Mode Function (aIMF), which is a derivation of Empirical Mode Decomposition (EMD), is proposed to remove white-Gaussian noise of foreign currency exchange rates that are nonlinear nonstationary times series signals. Noise patterns with different amplitudes and frequencies were randomly mixed into the five exchange rates. A number of filters, namely; Extended Kalman Filter (EKF), Wavelet Transform (WT), Particle Filter (PF) and the averaging Intrinsic Mode Function (aIMF) algorithm were used to compare filtering and smoothing performance. The aIMF algorithm demonstrated high noise reduction among the performance of these filters.<\/jats:p>","DOI":"10.3390\/a6030407","type":"journal-article","created":{"date-parts":[[2013,7,19]],"date-time":"2013-07-19T12:12:52Z","timestamp":1374235972000},"page":"407-429","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Noise Reduction for Nonlinear Nonstationary Time Series Data using Averaging Intrinsic Mode Function"],"prefix":"10.3390","volume":"6","author":[{"given":"Bhusana","family":"Premanode","sequence":"first","affiliation":[{"name":"Centre for Bio-Inspired Technology, Imperial College London, South Kensington,  London SW7 2AZ, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jumlong","family":"Vongprasert","sequence":"additional","affiliation":[{"name":"Ubon Rachathani Rajabhati Univeristy, 2 Ratchathani Road, Ubon Ratchathani 34000, Thailand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christofer","family":"Toumazou","sequence":"additional","affiliation":[{"name":"Centre for Bio-Inspired Technology, Imperial College London, South Kensington,  London SW7 2AZ, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2013,7,19]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Importance sampling approach for the nonstationary approximation error method","volume":"26","author":"Huttunen","year":"2002","journal-title":"Inverse Probl."},{"key":"ref_2","unstructured":"Brown, R.G., and Hwang, P.Y.C. 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