【摘要】 在传统的Fourier级数(FS)的基础上,提出了一种新的分数频FS(FFFS)的信号表示方法。该方法突破正交性要求下的频率为基频整数倍的限制,使得对信号的处理更加灵活、细致。首先给出了FFFS的定义,提出了获取分数频的试验法和二分频法;然后对压缩带宽、逼近项数、与原函数逼近度和Gibbs现象等性能与传统的FS进行比较,发现FFFS有相当的优越性。更多还原

【Abstract】 The Fourier series(FS) with fractional frequency intervals(FFFS) for the decomposition of signals is proposed.FFFS consists of sine and cosine functions,which is similar to FS,but the frequency intervals of the trigonometric functions don’t have to be integers.Therefore,the decomposition of signal by FFFS is more flexible and precise.Two algorithms to choose the best frequency intervals are put forward.Compared with FS,FFFS has better performance in frequency-width,approach-items,approach-precise and Gibbs phenomenon.更多还原