Efficient computation of the discrete autocorrelation wavelet inner product matrix
Efficient computation of the discrete autocorrelation wavelet inner product matrix
复制标题
离散自相关小波内积矩阵的高效计算
作者：
I. Eckley;G. Nason
离散自相关小波最近被应用于局部平稳时间序列的统计分析，用于局部谱的建模和估计。根据统计分析的需要，提出了离散交流小波内积矩阵的快速递归构造方法。该递归利用交流小波的双尺度性质将内积矩阵对角线上的相邻元素连接起来。递归方法是一个<s:2> (log (N)3)操作，它比蛮力方法所需的<s:2> (N log N)操作要好。最后，我们描述了二维（可分）情况下内积矩阵的一种有效构造。
Discrete autocorrelation (a.c.) wavelets have recently been applied in the statistical analysis of locally stationary time series for local spectral modelling and estimation. This article proposes a fast recursive construction of the inner product matrix of discrete a.c. wavelets which is required by the statistical analysis. The recursion connects neighbouring elements on diagonals of the inner product matrix using a two-scale property of the a.c. wavelets. The recursive method is an ↻(log (N)3) operation which compares favourably with the ↻(N log N) operations required by the brute force approach. We conclude by describing an efficient construction of the inner product matrix in the (separable) two-dimensional case.