The inner product matrix of discrete autocorrelation wavelets: efficient
computation and application.
Idris A. Eckley & Guy P. Nason
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 O(log(N)^3) operation which compares favourably with the
O(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.
Some keywords: LOCALLY STATIONARY TIME SERIES, EVOLUTIONARY WAVELET SPECTRUM,
DISCRETE AUTOCORRELATION WAVELETS, INNER PRODUCT MATRIX, INTERPOLATION SCHEMES.