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→The Solution: Spelling/Grammar Check, typos fixed: convertors → converters
The '''Nyquist-Shannon Sampling Criterion''', formulated by [[Harry Nyquist]] in 1928 and proven by [[Claude Shannon]] in 1949, states that each digital sample can be converted to a unique analog signal if the sampling rate is more than twice as large as the highest frequency in the signal. While Shannon's proof requires [[Fourier transform]]s, it can be deduced from the sequence of alias frequencies above. If <tt>g < 1/2 f<sub>s</sub></tt>, then f<sub>s</sub> is, by definition, greater than two times the sample's frequency. If <tt>g > 1/2 f<sub>s</sub></tt>, then <tt>f<sub>s</sub>-g</tt>, which is another alias, is less than one-half the frequency of sampling. Therefore, there is always one unique alias frequency less than 1/2 f<sub>s</sub>.
The '''Nyquist-Shannon Sampling Criterion''', formulated by [[Harry Nyquist]] in 1928 and proven by [[Claude Shannon]] in 1949, states that each digital sample can be converted to a unique analog signal if the sampling rate is more than twice as large as the highest frequency in the signal. While Shannon's proof requires [[Fourier transform]]s, it can be deduced from the sequence of alias frequencies above. If <tt>g < 1/2 f<sub>s</sub></tt>, then f<sub>s</sub> is, by definition, greater than two times the sample's frequency. If <tt>g > 1/2 f<sub>s</sub></tt>, then <tt>f<sub>s</sub>-g</tt>, which is another alias, is less than one-half the frequency of sampling. Therefore, there is always one unique alias frequency less than 1/2 f<sub>s</sub>.
Of course, every frequency always has aliases. However, digital-to-analog convertors assume that the sound has been recorded according to the Nyquist Criterion; therefore, they always play back the lowest alias.
Of course, every frequency always has aliases. However, digital-to-analog converters assume that the sound has been recorded according to the Nyquist Criterion; therefore, they always play back the lowest alias.
[[Category:Physics]]
[[Category:Physics]]