In his classic 1948 paper founding information theory, Claude Shannon offered the following generalization of the sampling theorem:
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Unser Cited Cheung-Marks paper in the most important developments of the sampling theorem in the last 50 years.
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MP3 files made with MPEG-2 don't have 20 kHz bandwidth because of the Nyquist Shannon sampling theorem.
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According to the sampling theorem, it is possible to reconstruct x ( t ) \ completely and exactly using the samples
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Somebody came in and added to this claim that the Nyquist Shannon sampling theorem is some kind of proof or confirmation.
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In digital applications, the number of pixels per line is an arbitrary choice as long as it fulfils the sampling theorem.
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The above is called the Paley Wiener Levinson theorem, which generalize WSK sampling theorem from uniform samples to non uniform samples.
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Shannon used Nyquist's approach when he proved the sampling theorem in 1948, but Nyquist did not work on sampling per se.
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The Nyquist sampling theorem says you need twice that for good reproduction-and you have two ears-so you need twice that.
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The Nyquist-Shannon sampling theorem provides an important guideline as to how much digital data is needed to accurately portray a given analog signal.
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