/sci/ - Science & Math

>>15089929
you need to sample at a rate of at least [math]2f[/math] to faithfully (kinda) capture a signal, where [math]f[/math] is the highest frequency contained in the signal. to capture a 1kHz sine wave, you need to sample at at least 2kHz. a square wave has infinitely high frequency components, so you can technically never truly capture a square wave, you can only be more and more reasonably certain its a square wave the higher you sample.
technically, you can never actually represent a continuous signal with discrete sampling. lets say you sample the peaks and troughs of a 1kHz sine wave (so youd be sampling at 2kHz). you could conclude that the signal is a 1kHz sine wave, but a sine wave of 2.5kHz would produce the exact same samples. these are called aliases, and the higher you sample, the farther out the aliases are; if you sample the 1kHz sine wave at 10kHz, the nearest alias is at 100kHz, i think. if youve ever seen video footage of something spinning really fast and noticed that the video made it look like it was spinning slowly, thats an example of aliasing.
https://en.wikipedia.org/wiki/Aliasing
https://en.wikipedia.org/wiki/Nyquist_frequency
https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem