Question

Now suppose that the chirp signal above is sampled at samples per second to create the discrete time signal fs=1000 cycles/second. At what time is the Nyquist criteria first violated?

Answer 1

The Nyquist criterion is violated when the frequency of a chirp signal exceeds half the sampling rate. For a sampling rate of 1000 samples per second, this occurs when the chirp signal frequency goes above 500 Hz.

Step-by-step explanation:

The question relates to the Nyquist criterion, which is fundamental in the field of signal processing, a branch of physics and electrical engineering. According to the Nyquist criterion, the sampling rate (fs) must be at least twice the highest frequency component in the signal to faithfully reconstruct the original analog signal. In the scenario where a chirp signal is being sampled at 1000 samples per second, as soon as the frequency of the chirp exceeds 500 Hz, the signal will violate the Nyquist criterion because it will not be sampled sufficiently to avoid aliasing.

Without information on the rate at which the chirp's frequency increases, it's not possible to give the exact time at which the Nyquist criterion is first violated. However, if we know the chirp begins at a frequency lower than 500 Hz and increases over time, the Nyquist criterion would be violated the moment the chirp frequency exceeds 500 Hz.