FM2let变换分解算法的研究

FM^2let变换分解力图采用最少的线性或非线性调频基函数来分解信号。FM^2let变换分解算法的基本原理是利用信号的瞬时频率求得FM^2let原子的5个参数，然后基于自适应匹配投影塔形分解思想实现FM^2let变换的分解。FM^2let变换分解算法在信号分析处理方面具有运算量小、运算速度快等优良的性能。FM^2let谱分辨率高、抗噪性能好、参数数据量少。并且利用伪时频分布可以去除交叉项干扰。理论和实验证明，FM^2let变换分解算法能对不同的信号结构表现出很强的适应性，能够简洁地表征信号时变或时不变特性。

Research on Decomposition Algorithm of FM2let Transform

A new decomposition algorithm named decomposition algorithm of FM^2let transform is developed to decompose a signal by using a simplest group of linear or nonlinear FM basis functions. Its basic principle is to find 5 parameters of FM^2let atom through estimation of instantaneous frequency, and then achieve the decomposition algorithm of FM^2let transform based on adaptive pyramidal matching projection algorithm. The decomposition algorithm of FM^2let transform has many excellent performances such as high calculation rate and low calculation capacity. It also has excellent features of high spectral resolution, good anti-noise performance and high compressibility, and can make cross-term free by using pseudo time-frequency distribution. Theoretical and experimental results show that the decomposition algorithm of FM^2let transform has strong adaptability to different signal structures and gives concise representation of time-variable or time-invariable characteristic of signal.