Why is the Nyquist frequncy on the bode diagrams the same as the sampling frequency?

I notice that when I create a discrete dynamical system with a given sampling frequency, and I plot the bode diagrams, the phase and amplitude responses are plotted up to the samping frequency. On the documentation page for the bode command, it calls this upper limit on the frequency the Nyquist frequency. Even in their example, this Nyquist frequency is exactly the same as the sampling frequency. They create a system with a sampling time of 0.5 seconds (2 Hz, or 6.28 rad/s) and the resulting bode diagrams go up to 6.28 rad/s. So why is this the case, when I know that the Nyquist frequency is defined as half of the sampling frequency?

[Star Strider]

Please give an example or a link.

[Nathan Sisson]

https://www.mathworks.com/help/control/ref/dynamicsystem.bode.html

Answer 1

[Voss]

I assume you're referring to something like this plot.

"sampling time of 0.5 seconds (2 Hz, or 6.28 rad/s)"

There's the problem. 2 Hz is 2*2*pi rad/s = 4*pi rad/s, which is approx 12.56 rad/s (not 6.28 rad/s).

Thus the corresponding Nyquist frequency is half of that or approx 6.28 rad/s.

[Nathan Sisson]

Ah yes. Basic math getting the best of me! Thank you.

[Voss]

You're welcome!