This project relies on sampling a waveform and then reconstructing it. The Shannon sampling theorem, which states that samples must be taken at a rate greater than twice the maximum frequency of the original signal (or at the Nyquist rate), is used so that no aliasing occurs. Aliasing occurs when a signal gets undersampled; a waveform of lower frequency will get reconstructed instead of the correct higher frequency signal. A picture is shown below to illustrate the idea:
Source: http://instruct1.cit.cornell.edu/courses/ee476/FinalProjects/s2010/egm23_lad97_rsw35/egm23_lad97_rsw35_website/egm23_rsw35_lad97_final_project_v2_files/image004.jpg
Therefore, in this project, the sampling rate is always set higher than 40 kHz (the oscilloscope functions correctly at a maximum frequency of 20 kHz). The A-to-D converter is responsible for sampling and has a maximum sampling rate of 2 megasamples/sec.
Read details of this project @ Digital Oscilloscope
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