In the realm of digital signal processing, undersampling occurs when the Nyquist theorem isn’t appropriately followed.
In simpler terms, undersampling happens when the sampling frequency is lesser than at least twice the maximum frequency in a signal.
Undersampling results in a loss of data and makes signal processing difficult for engineers.
Aliasing:
By far the biggest issue associated with undersampling is aliasing. In simple terms, aliasing is when two signals become indistinguishable from each other. This is also why they’re called ‘aliases’ of each other.
Generally speaking, aliasing can be of two types. Aliasing in signals sampled in time is called temporal aliasing (most commonly found in digital audio signals). Similarly, aliasing in spatially sampled signals is called spatial aliasing (most commonly found in low resolution pictures of intricate patterns).
Common Examples of Aliasing:
Aliasing is much more common than you think. We’ve all seen videos on YouTube where the camera’s frame rate (the rate at which it samples or records) syncs with a fast-moving object.
Some examples of aliasing include the extremely viral video of a bird flying without flapping its wings. To the average viewer that may seem like magic, but the answer to that problem is much simpler than that; aliasing is to blame for it!
Other common instances include the tires of a fast-moving car appearing stationary when being recorded with a low-end camera. Every time the camera samples the fast-moving object, in this scenario the tire, it appears at the same place with respect to its surroundings.
So, when you look back at the video, all you see is a stationary wheel when that’s not the case. The fast-moving wheels aren’t stationary at all but have taken up the alias of their stationary counterparts. That’s what aliasing is!
Avoiding Aliasing:
By far the easiest way of avoiding aliasing is following the Nyquist criteria. By making sure that the sampling frequency is greater than or at least equal to twice the maximum frequency component in a signal. Mathematically,
fs ≥ 2 fm
In doing so, we move away from undersampling and approach critical and oversampling. While there’s bandwidth wastage associated with oversampling, there’s no loss of data which makes it a much more reasonable option than undersampling!
Using Undersampling to Our Advantage:
Engineers have come up with ingenious methods of putting undersampling to good use. Undersampling can utilized to sample a signal above the Nyquist frequency. By limiting the bandwidth of a system by the help of a band pass filter, engineers are able to reconstruct the original input signal WITHOUT risking loss of information.
This works on the principle of Nyquist-Shannon sampling theorem, which states that the sampling frequency should be twice the bandwidth of the signal. Mathematically,
fs ≥ 2 (BW)
If that sounds way too complicated for you, you can always find pick up electrical components that avoid aliasing.
We at ADSANTEC have a large range of products with extremely wide bandwidths that go a long way in ensuring that there’s no aliasing. From limiting amplifiers to Boolean logic gates, we’ve all that you could ask for!