I presume we are all here well aware about foldback aliasing when sampling signals above the Nyquist frequency; i.e. half the sampling rate.
By contrast, the phenomenon of beating occurs when sampling a signal with a frequency slightly below the Nyquist frequency. You can see and hear some beats on this educational site.
Here is an example of a 60Hz signal sampled at 128Hz resulting in a 4Hz beat tone with a 8Hz beat. The beat tone frequency is calculated as follows: $f_{t}=\frac{f_{s}}{2}-f_{m}=\frac{128}{2}-60=4\,Hz$. The beat has a frequency twice this tone frequency.
In preparation of a paper, I am looking for a peer-reviewed or textbook reference about beating. I browsed through almost 20 DSP textbooks and found nothing.
On the web, I only found a Proceedings of the 2003 American Society for Engineering Education Annual Conference & Exposition session paper by Kostic which included the nice explanatory figure shown below. I am looking for something more authoritative though; peer-reviewed or textbook.
beat
orbeating
in relation to sampling. In a typical DSP application beating might be less a problem than foldback aliasing. However, this does not take away from the fact that both phenomena are of the same order and origin. In comparison, the alias frequency is $f_{a}=2\frac{f_{s}}{2}-f_{m}$. $\endgroup$intermodulation products
of an equivalentswitching sampling mixer
with a signum local oscillator at half the sampling frequency; i.e. the Nyquist frequency. A reference other than the referenced patent would equally interest me. $\endgroup$