Bandlimiting

Bandlimiting is the process of reducing a signal’s energy outside a specific frequency range, keeping only the desired part of the signal’s spectrum. This technique is crucial in signal processing and communications to ensure signals stay clear and effective. For example, it helps prevent interference between radio frequency signals, like those used in radio or TV broadcasts, and reduces aliasing distortion (a type of error) when converting signals to digital form for digital signal processing.

Bandlimited signals

A bandlimited signal is a signal that, in strict terms, has no energy outside a specific frequency range. In practical use, a signal is called bandlimited if the energy beyond this range is so small that it can be ignored for a particular purpose, like audio recording or radio transmission. These signals can be either random (unpredictable, also called stochastic) or non-random (predictable, known as deterministic).

In mathematical terms, a bandlimited signal relates to its Fourier series or Fourier transform representation. A generic signal needs an infinite range of frequencies in a continuous Fourier series to describe it fully, but if only a finite range is enough, the signal is considered bandlimited. This means its Fourier transform or spectral density—which show the signal’s frequency content—has “bounded support”, meaning it drops to zero outside a limited frequency range.

A bandlimited signal theoretically must extend in time from minus infinity to plus infinity with at least occasional non-zero patches, which is not the case in practical situations (see lower down).