Discrete generation algorithm and amplitude-frequency property of wavelet without analytic expression in various scales

作者：Zhao, Xue-Zhi^*; Ye, Bang-Yan; Chen, Tong-Jian

来源：Journal of Vibration Engineering, 2011, 24(5): 546-554.

• Amplitude frequency property
• Analytic expressions
• Daubechies Wavelet
• Discrete generation
• Generation algorithm
• Scale functions
• Time domain
• Wavelet function

To get the amplitude-frequency property of wavelet without analytic expression in the various scales, the discrete generation of wavelet in these scales in time domain should be solved firstly. The defect of one previous generation algorithm being pointed out and analyzed, a new algorithm is proposed based on multiresolution analysis theory, and the scale and wavelet functions in the various scales can be got by this new one using wavelet low pass filter coefficients. The amplitude-frequency property of No.2~10 Daubechies wavelets in the 5 scales is obtained by this algorithm, the results show directly that for these wavelets there are big overlaps among their frequency bands of the various scales, and furthermore for No.2~4 Daubechies wavelets there are some side segments in their frequency bands beginning from the third scale, while for No.9~10 Daubechies wavelets, the side segments disappear and their frequency overlap will also be certain reduced. Signal processing examples are presented to verify the accuracy of this kind of amplitude-frequency property.

• 出版日期2011-10
• 单位华南理工大学