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 x(t) = sin(2πft + θ). If this signal is sampled at a rate faster than fs > 2f so that we have the samples x(n / fs), where n is an integer, we can recover x(t) completely from these samples.
Similarly sums of sinusoids with different frequencies and phases are also bandlimited.
The deviation from unity between samples can be thought of as ``overshoot'' or ``ringing'' of the lowpass filter which cuts off at half the sampling rate, or it can be considered a ``Gibbs phenomenon'' associated with bandlimiting.
Figure 2: Bandlimited reconstruction of the signal The dots show the signal samples, the dashed lines show the component sinc functions, and the solid line shows the unique bandlimited reconstruction from the samples obtained by summing the component sinc functions.
The practical bandlimited interpolation algorithm presented below is based on the second interpretation.
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 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.
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