The discussion revolves around determining an appropriate sampling frequency to avoid aliasing for a given signal, specifically a triangle wave. Participants explore the implications of the Nyquist frequency and rate, as well as the challenges of systematic approaches to sampling in relation to the signal's frequency components.
Participants generally agree on the relevance of the Nyquist frequency and the challenges posed by the triangle wave's infinite frequency components. However, there is no consensus on the specific systematic approach to take or the implications of sampling frequency choices.
Participants note that the simple Nyquist sampling theorem assumes infinite sampling time, and there are more complex considerations for limited sampling times that are not commonly referenced.
Yes. I am familiar till the part that the maximum angular frequency is 8 rad/s. So using the Nyquist rate, the sampling frequency should be twice the max frequency. But I don't understand how to systematically approach this kind of question. Thank you.FactChecker said:
Sort of. You have a triangle wave, so theoretically, your sampling frequency needs to be infinite since there are frequency components going out to infinity. The way to approach it is to do a Fourier decomposition of the triangle wave and decide how well you need the reconstruction to resemble the triangle wave. Sampling at twice the frequency of the triangle wave will result in reconstructing a sine wave with the frequency of the triangle wave (ignoring aliasing). You need to sample at twice the highest frequency in the Fourier series you want to use to reconstruct the reconstruction of the triangle wave with the precision you require. Since any "real" triangle wave will have a finite bandwidth and not be a perfect triangle wave, you might start there.Electgineer said:
The figure shown is the frequency spectrum, not the wave. So it is much simpler.bobob said:
Oops... My mistake for not looking at the figure more closely...FactChecker said: