A fast wavelet-finite difference method is given to solve heat equation,applying the finite difference scheme and the orthonormal compactly supported wavelet transform approximation to the time and the space dimension of the heat equation for discrete and transformation.

The wavelet variance under the single scale is discussed,and in combining the information entropy in information theory with physical sense,the wavelet entropy under the multi-scale is introduced in this paper.

According to the properties of bias drift of optic gyro, the wavelet transform is used to study the wavelet variance of random process.

A long memory analysis method based on wavelet variance for time series was proposed.

With regard to the accuracy affection during fundamental component calculation caused by aperiodic component, frequency deviation and fractional harmonic in signal, the paper analyzes and compares three filter algorithms of Fourier algorithm, differential filter algorithm and shunt compensation algorithm.