# Does the Nyquist Sampling Theorem hold for a triangular wave?

Does the Nyquist Sampling theorem hold for a triangular wave produced by a function generator?

For example, a triangular wave with a frequency of 15 Hz sampled at 60 Hz, 180 Hz and 15000 Hz.

## 1 Answer

The Nyquist sampling theorem holds for bandlimited signals. Note that a perfect triangle wave is composed of a (convergent) infinite series of harmonics, which requires infinite bandwidth and is thus not bandlimited.

However, the energy remainder after a suffinciently large number of harmonics might be small enough than for a given noise floor that you can treat the portion of the triangle wave that is above that noise floor as bandlimited below some point above that last kept harmonic.

• The point is that it holds for any bandlimited signal. So, if you know you're dealing with a specific signal shape, and only need to estimate a few parameters of that, then less samples might do, but you couldn't reconstruct just any signal with less samples than Nyquist demands. – Marcus Müller Jan 22 '18 at 6:42