Purpose

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.

Design/methodology/approach

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 “spectrum analysis” of AGO/IAGO are carried out in the frequency domain.

Findings

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.

Practical implications

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.

Originality/value

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 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.

中文翻译：

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AGO / IAGO在频域的机理和滤波效果研究

目的

本文的目的是在频域上分析累加生成算子（AGO）/逆累加生成算子（IAGO）的机理和滤波效果。

设计/方法/方法

时域的AGO / IAGO将通过傅立叶变换转移到频域。基于灰色系统中AGO / IAGO的数学表达式与数字信号处理中数字滤波器的一致性，建立了AGO / IAGO的等效滤波器模型。AGO / IAGO数字信号处理系统“频谱分析”​​中的独特方法是在频域中执行的。

发现

通过理论研究和实例验证，说明了频谱分析的好处，并对AGO / IAGO的机理和滤波效果进行了定量分析。研究表明，AGO特别适合于系统的行为时间序列，其中长时间部分是主要因素。该动作序列具有良好的抗噪声效果。

实际影响

AGO / IAGO对某些统计数据的处理产生了奇妙的效果，例如，与经济增长，作物产量，气候和大气变化有关的大多数统计数据主要受长期因素（即低频数据）的影响，并且大多数干扰是短周期因素（高频数据）。经过1-AGO处理后，其高频成分被抑制，其低频成分被放大。从信息论的角度来看，这种双向效应大大提高了信噪比，并减少了新序列中的噪声/干扰比例。基于1-AGO演算，信息挖掘和外推预测将具有良好的效果。

创意/价值

作者发现1-AGO对数据序列的处理具有奇妙的效果。当1-AGO作用于数据序列X时，其低通滤波效果将有利于信息波动的消除和高频噪声/干扰的减少，因此数据显示出明显的指数变化趋势。但是，它不适合过度使用，因为其等效滤波器的极点处于非周期性含量。但是，由于零频率的pol效应，1-AGO将大大放大低频信息部分，同时抑制信息中的高频部分。