A linearFM (chirp) signal is an ideal test signal to explore the concept of aliasing due to sampling.
By visualizing the spectrogram of a synthesized chirp and listening to the sound, we experience the fact that a DtoC converter cannot create output signals with frequencies higher than one half of the sampling frequency.
Consult Section 42.5
Maximum Reconstructed Frequency for more discussion of this issue.
This chirp synthesis demo consists of two simple components (a CtoD converter and a DtoC converter) and four steps:

Use the mathematical formula for a continuoustime chirp signal
$$
x(t) = \cos( \pi\alpha t^2 )\qquad 0\leq t \leq T
$$
to define a signal whose chirp rate is \(\alpha\)Hz/s, whose duration is \(T\) seconds.

Produce a discretetime signal by sampling \(x(t)\) at a rate \(f_s\) samples/s.
This is done by evaluating \(x(t)\) at \(t=n/f_s\), and is, in effect, a CtoD converter.
The result is \(x[n] = x(n/f_s)\).

Use Matlab's
soundsc
function to play the signal for listening.
This is the DtoC conversion component because a continuoustime signal must be created from \(x[n]\) in order to drive the audio output, i.e., the speakers.

Evaluate and display the spectrogram of \(x[n]\), which gives a visualization of what we hear.
In the demo, the chirp rate is \(\alpha = 1000\) Hz/s, and the time duration is \(T=3\)s, so the instantaneous frequency \((f_i(t) = \alpha t)\) goes from zero at \(t=0\) to \(3\alpha = 3000\)Hz at \(t=3\)s.
Since the highest frequency in \(x(t)\) is \(3000\)Hz, there should be no aliasing if \(f_s\geq 6000\)Hz.
The demo shows what happens for five different sampling frequencies: 8000, 6000, 4000, 3000, and 2400 Hz.
The first two cases exhibit no aliasing and the sound rises from 0 to 3000 Hz.
In the last three cases, the sound goes up and down because \(f_s/2<3000\)Hz.
When \(f_s=4000\), the maximum output frequency is \(2000\)Hz, for \(f_s=3000\), the maximum output frequency is \(1500\)Hz, and for \(f_s=2400\), the maximum output frequency is \(1200\)Hz.
Spectrograms for the five cases are shown below. Click on the spectrogram to hear the
corresponding chirp.
Note the different \(y\)axis scales for frequency.
When you listen to the sounds, try to follow the ups and downs that match the spectrograms.