DFT对FT近似中的时域混叠现象研究

Analysis of Time Folding Phenomenon when Using DFT Approximating FT

根据傅里叶性质可知,信号的时宽和带宽不可能同时缩小,也不能同时扩大.二者也不可能同为有限值.若信号的时间长度有限,当进行时域抽样时,频域必然发生混叠;反之,若信号的频带宽度有限,当进行频域抽样时,时域必然发生混叠.从理论上侧重分析了DFT对FT近似中的时域混叠现象,给出了当频域抽样点数小于原序列长度时,时域混叠的计算规律.

According to the character of Fourier,it is impossible for the time length and frequency bandwidth of signal to be shorten or extended simultaneously.And it is impossible for them to be limited value at the same time.That is to say that if the time length of signal is limited,the frequency bandwidth of signal will be unlimited when sampling in time domain,the frequency folding phenomenon will certainly happen.Contrarily,if the frequency bandwidth of signal is finite,the time length of signal will be infinite when sampling in frequency domain,the time folding phenomenon will certainly happen.The time folding phenomenon is analyzed,when using DFT approximating FT.Furthermore,the algorithm is provided to reader when (sampling number in frequency domain)<(the length of the original sequence).