{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T18:10:03Z","timestamp":1754158203584,"version":"3.41.2"},"reference-count":47,"publisher":"Emerald","issue":"1","license":[{"start":{"date-parts":[[2020,5,26]],"date-time":"2020-05-26T00:00:00Z","timestamp":1590451200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["GS"],"published-print":{"date-parts":[[2020,5,26]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to analyze the mechanism and filter efficacy of accumulation generation operator (AGO)\/inverse accumulation generation operator (IAGO) in the frequency domain.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>The AGO\/IAGO in time domain will be transferred to the frequency domain by the Fourier transform. Based on the consistency of the mathematical expressions of the AGO\/IAGO in the gray system and the digital filter in digital signal processing, the equivalent filter model of the AGO\/IAGO is established. The unique methods in digital signal processing systems \u201cspectrum analysis\u201d of AGO\/IAGO are carried out in the frequency domain.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>Through the theoretical study and practical example, benefit of spectrum analysis is explained, and the mechanism and filter efficacy of AGO\/IAGO are quantitatively analyzed. The study indicated that the AGO is particularly suitable to act on the system's behavior time series in which the long period parts is the main factor. The acted sequence has good effect of noise immunity.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Practical implications<\/jats:title><jats:p>The AGO\/IAGO has a wonderful effect on the processing of some statistical data, e.g. most of the statistical data related to economic growth, crop production, climate and atmospheric changes are mainly affected by long period factors (i.e. low-frequency data), and most of the disturbances are short-period factors (high-frequency data). After processing by the 1-AGO, its high frequency content is suppressed, and its low frequency content is amplified. In terms of information theory, this two-way effect improves the signal-to-noise ratio greatly and reduces the proportion of noise\/interference in the new sequence. Based on 1-AGO acting, the information mining and extrapolation prediction will have a good effect.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>The authors find that 1-AGO has a wonderful effect on the processing of data sequence. When the 1-AGO acts on a data sequence <jats:italic>X<\/jats:italic>, its low-pass filtering effect will benefit the information fluctuations removing and high-frequency noise\/interference reduction, so the data shows a clear exponential change trends. However, it is not suitable for excessive use because its equivalent filter has poles at the non-periodic content. But, because of pol effect at zero frequency, the 1-AGO will greatly amplify the low-frequency information parts and suppress the high-frequency parts in the information at the same time.<\/jats:p><\/jats:sec>","DOI":"10.1108\/gs-01-2020-0014","type":"journal-article","created":{"date-parts":[[2020,5,26]],"date-time":"2020-05-26T07:35:57Z","timestamp":1590478557000},"page":"1-21","source":"Crossref","is-referenced-by-count":3,"title":["Study on mechanism and filter efficacy of AGO\/IAGO in the frequency domain"],"prefix":"10.1108","volume":"11","author":[{"given":"Changhai","family":"Lin","sequence":"first","affiliation":[]},{"given":"Zhengyu","family":"Song","sequence":"additional","affiliation":[]},{"given":"Sifeng","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Yingjie","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Jeffrey","family":"Forrest","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2021021515241207900_ref001","first-page":"95","article-title":"Realization of digital filters","volume":"AU-20","year":"1972","journal-title":"IEEE Trans. Audio Electroacoust"},{"volume-title":"Fourier Analysis of Time Series: An Introduction","year":"1976","key":"key2021021515241207900_ref002"},{"volume-title":"Signals, Systems, and Transforms","year":"2008","key":"key2021021515241207900_ref003"},{"key":"key2021021515241207900_ref004","first-page":"1","article-title":"Time-delayed polynomial grey system model with the fractional order accumulation","volume":"2018","year":"2018","journal-title":"Mathematical Problems in Engineering"},{"issue":"12","key":"key2021021515241207900_ref005","first-page":"122","article-title":"Times cumulative grey model with residual correction","year":"1997","journal-title":"System Engineering - Theory and Practice"},{"volume-title":"Grey Control System","year":"1985","key":"key2021021515241207900_ref006"},{"issue":"5","key":"key2021021515241207900_ref007","first-page":"7","article-title":"The grey exponential law of cumulative generation- Optimal information processing of grey control system","year":"1987","journal-title":"Journal of Huazhong University of Science and Technology"},{"volume-title":"Signals and Systems","year":"2001","key":"key2021021515241207900_ref008"},{"volume-title":"Fourier Series, Encyclopedia of Mathematics","year":"1994","key":"key2021021515241207900_ref009"},{"issue":"6","key":"key2021021515241207900_ref010","first-page":"147","article-title":"Generalized cumulative grey predictive control model and its optimization algorithm","volume":"29","year":"2009","journal-title":"System Engineering - Theory and Practice"},{"issue":"4","key":"key2021021515241207900_ref011","first-page":"323","article-title":"Comparison of the characteristics of grey models by direct modeling and cumulative modeling respectively","year":"1999","journal-title":"Journal of Wuhan University of Water Resources and Electric Power (Yichang)"},{"volume-title":"Theory and Application of the Z-Transform Method","year":"1964","key":"key2021021515241207900_ref012"},{"issue":"2","key":"key2021021515241207900_ref013","first-page":"260","article-title":"(1,1|sin) model based on fractional accumulation and its application","volume":"39","year":"2019","journal-title":"Mathematics Magazine"},{"issue":"4","key":"key2021021515241207900_ref014","first-page":"111","article-title":"On spectrum analysis of different weakening buffer operators","volume":"31","year":"2019","journal-title":"Journal of Grey System"},{"issue":"1","key":"key2021021515241207900_ref015","first-page":"39","article-title":"The three axioms of buffer operator and their application","volume":"3","year":"1991","journal-title":"Journal of Grey System"},{"edition":"8th ed.","volume-title":"Grey Systems: Theory and Applications","year":"2017","key":"key2021021515241207900_ref016"},{"volume-title":"Grey Systems: Theory and Applications","year":"1991","key":"key2021021515241207900_ref017"},{"issue":"5","key":"key2021021515241207900_ref018","first-page":"976","article-title":"Model identification algorithm based on Grey accumulation and weighted product","volume":"32","year":"2010","journal-title":"Journal of System Engineering and Electronics"},{"volume-title":"Grey Systems: Theory and Applications","year":"2011","key":"key2021021515241207900_ref019"},{"issue":"4","key":"key2021021515241207900_ref020","first-page":"1033","article-title":"Fractional order reverse accumulation NHGM (1,1, K) model and its application","volume":"36","year":"2016","journal-title":"System Engineering - 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