门函数时域离散与模拟傅里叶变换误差分析

给出了由离散信号频谱求解模拟信号频谱的过程,通过门函数的傅里叶变换分析了其频域与抽样序列的傅里叶变换的误差来源,并通过实例验证了该误差。对连续信号抽样造成频谱混叠是模拟信号傅里叶变换和离散信号傅里叶变换误差的根源,要想消除其误差,必须满足时域抽样定理。门函数频谱中频率是区域无穷大的,所以针对特殊波形造成的这种误差是不可避免的。

Discrete Gate Function in Time Domain and Error Analysis of Simulated Fourier Transform

The process of calculating analog signal spectrum from discrete signal spectrum is given. The error sources of Fourier transform in frequency domain and sampling sequence are analyzed by Fourier transform of gate function, and the error is verified by an example. Frequency spectrum aliasing caused by continuous signal sampling is the root of the error of Fourier transform of analog signal and discrete signal. To eliminate the error, the sampling theorem in time domain must be satisfied. The frequency of gate function spectrum is infinite, so the error caused by special waveform is inevitable.