Construction Of Multiwavelets With Optimum Time-frequency Resolution

Wavelet transform is attracting much attention from mathematicians and engineers for its excellent time-frequency character. The research of multiwavelet is an important branch of wavelet theory. Multiwavelet is better than traditional wavelet because it can has the attribute of symmetry and orthogonality, compact support and high vanishing moment accompanied. In order to improve time-frequency resolution, this paper has made a research on how to construct a family of optimum time-frequency resolution(OPTFR) multiwavelet.The OPTFR multiwavelets constructed by former researchers have many shortcomings. First, they have only 2 orders of vanishing moment. Second, since the optimum result is found by Simplex Search Algorithm, it can not make most certain that it can find the optimum result. Third, former researches have not referred to OPTFR multiwavelets with different support length.Based on former researches, this paper proposed a method which integrated cascade algorithm and the former methods. We solved the parameters in vanishing moment conditions or balanced conditions by genetic algorithm, the Newton method and the secant method. Finally, we constructed two kinds of OPTFR multiwavelets that satisfied 2, 3 or 4 orders vanishing moment respectively:(1) The multiwavelets with the same support as the former ones, and with more smoothness and better time-frequency resolution. And the balanced multiwavelets obtained by"first balanced then optimum"method.(2) The OPTFR balanced multiwavelets with different support.