| 小波和傅里叶变换在坐标时间序列分析中的应用 |
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| 引用本文： | 蔡富,孙付平,戴海亮,朱新慧,张龙龙.小波和傅里叶变换在坐标时间序列分析中的应用[J].全球定位系统,2019,44(4):40-46. |
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| 作者姓名： | 蔡富 孙付平 戴海亮 朱新慧 张龙龙 |
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| 作者单位： | 信息工程大学 地理空间信息学院, 河南 郑州 450001 |
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| 摘 要： | 正确提取坐标时间序列中的特征信息是非线性变化分析的前提．根据傅里叶变换和小波变换各自的特点,提出将两种方法结合起来对时间序列在时域和频域上进行分析的算法．首先采用小波函数db4对坐标时间序列分解5层得到高频和低频部分,进而分析各次谐波的时域波形以及可能存在的突变信息和区间,再在快速傅里叶变换的基础上求得各次谐波的准确频率和幅值．研究结果表明,低频分析可以直观地得到“周年项”和“两年周期项”,而高频分析能够较准确提取“半周年项”、“一季项”等短周期．与单独采用傅里叶变换或小波变换相比,基于小波变换与傅里叶变换相结合的方法能够有效地提取坐标时间序列中的特征信息,具有较高的研究价值.
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| 关 键 词： | 时间序列 非线性变化 小波变换 傅里叶变换 多分辨率分析 |
Application of wavelet and Fourier transform in? time series analysis |
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| Affiliation: | Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, China |
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| Abstract: | Exactly decomposing the feature information of time series is the precondition to non linear variation analysis. According to the characteristics of Fourier and wavelet transform, two methods are integrated and applied to analyze time series in time domain and frequency domain, and comprehensive algorithm of wavelet and Fourier transform is presented. Firstly, the wavelet function DB4 is used to decompose the coordinate time series into five layers to get the high frequency and low frequency parts. Then, the time domain waveforms of each harmonic and the possible sudden change information and intervals are obtained. Finally, the exact frequency and amplitude of each harmonic are obtained on the basis of fast Fourier transform. The results show that the low-frequency analysis can intuitively obtain the “annual term” and “two-year cycle term”, while the high-frequency analysis is consistent with the extraction of short-term cycles such as “semiannual term” and “one-season term”. So the method based on wavelet transform and Fourier transform has many advantages compared with Fourier transform and wavelet transform alone, it can effectively extract the feature information of station time series, and has a big research value. |
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