The spectrum of the sampled signal is a periodic copy of the spectrum of the original continuous-time signal (of course, the sampling must satisfy Nyquist theorem). If the sampling period is f, the frequency spectrum of the sampled signal becomes periodic, the period is f, the amplitude becomes f times the original, and the shape of one period is the same as that of the continuous signal.

Then the spectrum of the sampled discrete signal should [satisfy the sampling theorem] reflect the spectrum of the original analog signal, otherwise the sampling is meaningless. The sampled spectrum is a periodic spread of the original spectrum. In practical application, it is necessary to filter out the original components above the useful frequency as much as possible and increase the sampling frequency to reduce spectrum aliasing.

Extended data:

Sampling, also known as sampling, is the signal discretization in time, that is, the instantaneous value of the analog signal x(t) is taken point by point according to a certain time interval △ t, which is realized by multiplying the sampling pulse with the analog signal.

The selection of sampling interval is confused with signal: when sampling analog signal, the sampling interval must be determined first. How to choose △t reasonably involves many technical factors that need to be considered. Generally speaking, the higher the sampling frequency, the denser the sampling points, and the closer the discrete signal is to the original signal.

However, an excessively high sampling frequency is not desirable. For a signal with a fixed length (t), too much data (N=T/△t) is collected, which increases the unnecessary calculation workload and storage space of the computer. If the amount of data (n) is limited, the sampling time is too short, which will lead to the exclusion of some data information.

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