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在工程信号分析中,有时会遇到被分析信号是密集型窄带频谱的情况,这时通常只能采用频率细化技术,进行大数据量的采样和计算才能识别出信号中细微的频率成分。本文针对这类信号频带宽有限的特点,研究了其采样频率和采样信号频谱混叠之间的关系,发现当以远远小于信号中最高频率成分的两倍,但又大于信号带宽的两倍的某些频率对信号进行采样时,采样信号虽然产生了严重的频混,但其频谱形状并未失真,只是在频率轴上偏移了一段距离。作者对这种特殊的频混现象加以利用,提出了一个无频谱形状失真的带通信号采样公式和一种简便的带通信号频率细化分析方法。文中对如何将有频混的带通采样信号恢复为无频混的常规信号问题也进行了讨论。
In engineering signal analysis, sometimes it is the case that the analyzed signal is an intensive narrow-band frequency spectrum. In this case, only the frequency thinning technique can usually be used to sample and calculate a large amount of data to identify the subtle frequency components in the signal. In this paper, the relationship between the sampling frequency and aliasing of the sampled signal is studied in this paper because of the limited bandwidth of the signal. It is found that when the signal frequency is much less than twice the highest frequency component of the signal but more than twice the signal bandwidth When sampling a signal at some frequencies, the sampled signal, despite its severe frequency mixing, does not distort the shape of the spectrum but is offset by a distance on the frequency axis. The author makes use of this special phenomenon of frequency mixing and presents a sampling formula of bandpass signal without spectral shape distortion and a simple frequency thinning analysis method of bandpass signal. This paper also discusses how to restore the mixed signal with frequency-mixed bandpass signal to the conventional signal without frequency-mixing.