【摘要】 分数计算———分数阶微分与分数阶积分受到众多领域的广泛关注。从信号处理的观点来考察分数阶微分问题。首先 ,在频域中将微分算子分解为幅度算子和相位算子 ,导出正弦、余弦和复指数信号的分数阶微分表达式 ;然后考察矩形、三角形、梯形等常用周期信号的分数阶微分。给出了一些常用周期信号分数阶微分的解析形式 ,同时也研究了周期序列的分数阶微分运算的数字实现。结果表明分数微分运算确实存在 ,它同时改变了信号的幅度和相位 ,可以对之进行非线性分析。更多还原

【Abstract】 The fractional calculus-fractional differentiation and fractional integration are widely paid attention in many fields in recent years.The fractional order derivative is investigated from the viewpoint of signal processing in this paper. Firstly, in the frequency domain, differentiatial operator is decomposed into magnitude and phase operator, and the fractional order expressions of periodical signals, such as sine wave, cosine wave and complex exponent signal, are deduced. Secondly, the fractional order differentiation of rectangle signal, triangle signal and trapezia signal are carried out, meanwhile the analytical expressions of them are presented in this paper. Finally, digital realization of fractional order differentiation is investigated. The experimental result shows that the fractional order differentiation does exist, and it can be used in non-linear analyse of signals.更多还原