Bandlimited Functions
Actual signals have finite duration and their frequency content, as defined by the Fourier transform, has no upper bound. Some amount of aliasing always occurs when such functions are sampled. Functions whose frequency content is bounded (bandlimited) have infinite duration. If sampled at a high enough rate, determined by the bandwidth, the original function can in theory be perfectly reconstructed from the infinite set of samples.
Read more about this topic: Aliasing
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“Empirical science is apt to cloud the sight, and, by the very knowledge of functions and processes, to bereave the student of the manly contemplation of the whole.”
—Ralph Waldo Emerson (1803–1882)