The discussion centers on the Nyquist frequency and the Nyquist rate, specifically in relation to sampling a triangle wave with a maximum angular frequency of 8 rad/s. To avoid aliasing, the sampling frequency must be at least twice the maximum frequency, which is 16 Hz in this case. The conversation emphasizes the importance of Fourier decomposition for accurately reconstructing the triangle wave, noting that real triangle waves have finite bandwidths. Additionally, it highlights the theoretical need for infinite sampling frequency due to the infinite frequency components of a triangle wave.
PREREQUISITESSignal processing engineers, audio engineers, and anyone involved in digital signal analysis or reconstruction will benefit from this discussion.
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: