Bandlimited

From Academic Kids

A bandlimited signal is a deterministic or stochastic signal (e.g., function of time) whose Fourier transform, or power spectrum are zero after a certain frequency. This has the consequence that the signal can be fully reconstructed from its samples, provided that the sampling frequency is at least twice as much as the maximum frequency in the bandlimited signal. This critical frequency is also referred to as the Nyquist frequency. This result is known as the sampling theorem, and usually attributed to Nyquist or Shannon and referred to as Nyquist-Shannon Sampling Theorem.

An example of a simple deterministic bandlimited signal is a sinusoid of the form <math>x(t) = \sin(2 \pi ft + \theta) <math>. If this signal is sampled at a rate faster than <math>f_s > 2f <math> so that we have the samples <math>x(n/f_s)<math>, where <math>n<math> is an integer, we can recover x(t) completely from these samples.

Similarly sums of sinusoids with different frequencies and phases are also bandlimited.

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