During the conversion of analog/digital signals, when the sampling frequency fs.max is greater than twice the highest frequency fmax in the signal (fs.max>2fmax), the digital signal after sampling completely retains the information in the original signal. In general practical applications, the sampling frequency is guaranteed to be 2.56 to 4 times the highest frequency of the signal; sampling theorem is also called Nyquist Theorem . [1]
The sampling theorem was proposed by ET Whittaker (1915), Kotelnikov (1933), and Shannon (1948). In the field of digital signal processing, the sampling theorem is a basic bridge between continuous-time signals (often called "analog signals") and discrete-time signals (often called "digital signals"). This theorem explains the relationship between the sampling frequency and the signal spectrum , and is the basic basis for the discretization of continuous signals . It establishes a sufficient condition for a sampling rate that allows a sequence of discrete samples to capture all information from a bandwidth-limited continuous-time signal.
The sampling theorem stipulates that the sampling frequency must be greater than twice the highest frequency of the signal of interest (that is, the analysis frequency), otherwise frequency aliasing will occur. However, since the anti-aliasing filter of the analog circuit cannot reach the steepness of the ideal filter, the sampling frequency is generally taken as 2.56 times the analysis frequency.
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