Abstract
This paper describes the transition from analog to digital signals, and the relationship between the angular frequency of continuous-time signals and the digital angular frequency of discrete-time signals. In this paper, the frequency domain expression of the signal after the upper sampling (interpolation) and down sampling (decimation) of the digital signal is strictly derived theoretically. In the frequency domain, the spectrum of the L-sampled signal can be obtained by shrinking the original signal spectrum by L times, the amplitude is constant, and the image frequency is generated within the original period length. Under the premise that no signal distortion occurs under M times, the frequency domain is widened by M times relative to the original signal frequency domain, and the amplitude changes nonlinearly. In this paper, MATLAB is used to perform up-and down-sampling and distortion processing on sound signals to verify the correctness of theoretical frequency domain changes.
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