中国传媒大学学报(自然科学版)2023,Vol.30Issue(2) :76-84.DOI:10.3969/j.issn.1673-4793.2023.02.010

累加卷积变换及其在灰色预测模型中的应用

The accumulative convolution transform and its application in grey forecasting model

陈涛
中国传媒大学学报(自然科学版)2023,Vol.30Issue(2) :76-84.DOI:10.3969/j.issn.1673-4793.2023.02.010

累加卷积变换及其在灰色预测模型中的应用

The accumulative convolution transform and its application in grey forecasting model

陈涛1
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作者信息

  • 1. 中国传媒大学数据科学与智能媒体学院,北京 100024
  • 折叠

摘要

基于数据序列卷积运算提出了一种构建累加生成算子的新途径.通过构造一种累加生成卷积序列来实现数据序列的累加生成.然后引入单边Z变换,得到累加生成卷积序列在频率域的形式,从而得到累加生成算子在频率域的表达式.对于逆累加生成算子,构造了相应的逆累加生成卷积序列,并导出它在频率域的表达式.通过构造累加生成卷积序列和单边Z变换得到其频率域的表达式,获得两个全新的视角来理解累加生成算子和逆累加生成算子之间的互逆关系.最后通过实际案例验证了理论的正确性和方法的有效性.

Abstract

Based on the convolution methods,this paper propose a new method to construct the accumulative generation operator.A data sequence called accumulative generation convolution sequence is constructed,which play the same role as accumulative generation operator.Through the single side Z-transform,the accumulative convolution sequence in the complex field is obtained,which is the expression of the accumulative generation operator in the frequency domain.The similar results of the inverse accumulative generation operator are also developed.Finally,we obtain two new points of view to interpret the mutually inversion relationships between the accumulating operator and the inverse accumulating generation operator.Finally,some real cases are demonstrated to verify the accuracy of the theoretical results and the effectiveness of the method.

关键词

灰色系统理论/灰色预测模型/微分方程/参数估计/Z变换

Key words

grey system theory/grey forecasting model/differential equation/parameter estimation/Z-transform

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基金项目

中央高校基本科研业务费专项中国传媒大学项目(CUC220B005)

出版年

2023
中国传媒大学学报(自然科学版)
中国传媒大学

中国传媒大学学报(自然科学版)

CHSSCD
影响因子:0.514
ISSN:1673-4793
被引量1
参考文献量3
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