信号的瞬时参数与正交小波基

对于可表成ｕ（ｔ）＝ａ（ｔ）ｃｏｓθ（ｔ）的信号，称ａ（ｔ）为其瞬时振幅，θ（ｔ）为瞬时位相，为瞬时频率．在许多实际问题中，瞬时振幅、位相、频率等瞬时参数的提取有重要意义．但已知的一些瞬时参数计算方法均各有其局限性．本文构造了一种频谱支集紧且有解析表达式的小波，利用它得到一种计算信号瞬时参数的能抗噪声干扰的快速、局部算法．理论分析和数值模拟的结果表明，该方法是实用而有效的，可望能满足许多实际问题的需要．

INSTANTANEOUS PARAMETERS OF SIGNALS AND ORTHOGONAL BASES OF WAVELETS

A real signal can be written in the form u（t） = a（t）cosθ（t）, where a（t） isthe instantaneous amplitude of u（t）, θ（t） the instantaneous phase, and theinstantaneous frequency. In many practices, the extraction of such instantaneousparameters as instantaneous amplitude, phase and frequency, is quite important Theexisting methods for calculation of instantaneous parameters all have some defects. Inthis papef, we construct a kind of wavelet each of which has compact support in thefrequency domain, and Fourier transform of foe wavelet has analytic representation.Using these wavelets, we obtain a fast local and anti-noise algorithm for calculationof instantaneous parameters of signal. Theoretical analysis and numerical simulationsshow that our method is practical and efficient. It is believed that the method canmeet the needs of many practical fields.