小波分析方法及其電力應用(編輯修改稿)
2025-01-19 03:56 本頁面
【文章內容簡介】 rencezFourier Transform180。s sine and cosine functions couldn180。t provide time information. zWavelet functions are localized in time domain. zWindowed Fourier transform uses the same square window for all frequencies, the resolution is the same at all locations in the timefrequency plane.WFT and Wavelet DifferenceWFT and Wavelet DifferencezWavelet transform180。s window could vary. For example, it uses long timewindow for lowfrequency signal and short timewindow for highfrequency signal. 4. 連續(xù)小波變換（ CWT ）zContinuous Wavelet Function（連續(xù)小波函數）zDilation, contraction and translation of wavelets （小波的伸縮和平移）zContinuous Wavelet Transform（連續(xù)小波變換）zInverse CWT （連續(xù)小波逆變換）z參考： MATLAB的小波工具箱連續(xù)小波函數z The dilation, contraction （伸縮） and translation （平移） of mother wavelet results in a set of continuous wavelets:z a is called scale factor（尺度因子，與頻率有關）z b is called translation factor（平移因子，與時間有關）伸縮和平移連續(xù)小波變換zFor signal f (t) ? L2(R) , its continuous wavelet transform (CWT) is:zWherezWf(a,b) is continuous wavelet coefficient （連續(xù)小波系數）CWT 示例連續(xù)小波逆變換zSignal f (t) can be reconstructed（重構） by its continuous wavelet coefficients:zThis is called Inverse Continuous Wavelet Transform.MATLAB的小波工具箱zwavemenu5. 離散小波變換（ DWT ）zDrawback of CWT （連續(xù)小波變換的缺點）zDiscrete Wavelet Transform （離散小波變換） ......zExample: EMI noise analysis （示例： EMI信號分析） 連續(xù)小波變換的缺點zContinuous wavelet functions are correlated.zMathematically speaking, the wavelet functions are not an orthogonal base （不是正交基） .基，正交基zIn a 2Dimension space, there are 3 vectors :zThe following is an orthogonal base:連續(xù)小波變換具有冗余性zContinuous wavelet trans
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