小波的尺度离散化与稳定性研究

在使用小波变换重构信号的应用中,为了计算处理方便及克服冗余性,常采用离散化处理。为确定均匀点格动态采样网络下的尺度采样间隔的取值及其与小波稳定性的关系,本文分别用Morlet小波和Marr小波对信号进行均匀离散小波变换。对于Morlet小波,其尺度采样间隔有一个取值区间,在这个区间内取值既能分析数字信号的最高频率及避免频谱混叠,又能保证小波的稳定性;而对于Marr小波,其尺度采样间隔的取值不能同时保证分析数字信号的最高频率和维持小波的稳定性,即稳定性与频率选择性是一对矛盾,但在二进抽取采样下选择适当的尺度伸缩因子可缓解这一矛盾。

Research on the Wavelet' s Scale Discreteness and Stability

For the purpose of calculating convenience and overcoming redundancy, discreteness always is adopted in the application of reconstructing signal through wavelet transform. Under the equality of sampling, Morlet wavelet and Marr Wavelet are adopted to cany through signal' s equal discrete wavelet transform in order to confirm the relation between choosing scale sample space and wavelet' s stableness. To Morlet wavelet, it can analyze the highest frequency of digital signal and avoid spectrum's overlapping, moreover, it is stable when scale sample space is in a section; But to Marr wavelet, the section can' t be found because wavelet' s stability must be maintained at the same time analyzing the highest frequency of digital signal, in other words, the stableness and frequency selectivity of wavelet contradict each other in wavelet analysis, But this problem can be mitigated to some extend by changing the scaling dilation parameter under binary draw - out scale sampling.