关键词: 白噪声, 频带重叠, 统计模拟, 无显式小波, 小波分解

Abstract: To make clear the overlap extent of frequency band of wavelet without analytic expression between the two adjacent scales, white noise is proposed as the input signal of wavelet transform, and the principle that white noise is utilized to obtain the amplitude-frequency property of wavelet is analyzed, and by combining with statistical simulation, an algorithm to compute the amplitude-frequency property of wavelet without analytic expression in dyadic scales is put forward. The frequency windows of No.2~10 Daubechies wavelets in 5 dyadic scales are achieved by this algorithm, which visually display the overlap status of frequency band of these wavelets between the two adjacent scales. The overlap area of frequency band between the two adjacent scales is computed quantitatively, and the results show that for Daubechies wavelet series, when number of wavelet increases, overlap area of frequency band will decrease monotonously and the effect of signal isolation of wavelet will improve. By the study on the overlap area ratio, it is further found out that, for the two adjacent scales of each Daubechies wavelet, the proportion of overlap area in frequency window of small scale is smaller than that of the big scale, and generally the overlap area ratio of the big scale is the double of that of the small scale.

Key words: Frequency band overlap, Statistical simulation, Wavelet decomposition, Wavelet without analytic expression, White noise