PurposeThe 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.Design/methodology/approachThe 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 “spectrum analysis” of AGO/IAGO are carried out in the frequency domain.FindingsThrough 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.Practical implicationsThe 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.Originality/valueThe authors find that 1-AGO has a wonderful effect on the processing of data sequence. When the 1-AGO acts on a data sequence X, 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.
[1]
Ramesh Chandra Agarwal,et al.
ON REALIZATION OF DIGITAL FILTERS
,
1974
.
[2]
Nannan Ma,et al.
Time-Delayed Polynomial Grey System Model with the Fractional Order Accumulation
,
2018,
Mathematical Problems in Engineering.
[3]
Sifeng Liu,et al.
Using fractional order accumulation to reduce errors from inverse accumulated generating operator of grey model
,
2014,
Soft Computing.
[4]
L. A. Zadeh,et al.
The analysis of sampled-data systems
,
1952,
Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.
[5]
Tong Xiao.
On AGO Effect of the Grey Model
,
2002
.
[6]
Wei Meng,et al.
Study on fractional order grey reducing generation operator
,
2016,
Grey Syst. Theory Appl..
[7]
Sourav Pradhan,et al.
Corrigendum #2 to “On Synergistic Integration of Adaptive Dithering Based Internal Model Control for Hysteresis Compensation in Piezoactuated Nanopositioner”
,
2015,
Mathematical Problems in Engineering.
[8]
Wei Cui,et al.
Non-homogenous discrete grey model with fractional-order accumulation
,
2014,
Neural Computing and Applications.
[9]
Sifeng Liu,et al.
Grey system model with the fractional order accumulation
,
2013,
Commun. Nonlinear Sci. Numer. Simul..
[10]
Zhengxin Wang,et al.
A Fourier residual modified Nash nonlinear grey Bernoulli model for forecasting the international trade of Chinese high-tech products
,
2015,
Grey Syst. Theory Appl..