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<div style="position:absolute; z-index:-1;position:absolute; top:-100px; right:-500px; ">[[File:President Barack Obama.jpg]]</div>'''Aliasing''' is a problem with [[digital]] sampling of [[analog]] waveforms, such as [[sound]] waves.  When the digital sample is converted back to an analog waveform - such as when a [[CD]] is played - the player will emit the lowest '''alias''' waveform, which might not be the sound actually recorded.

'''Aliasing''' is a problem with [[digital]] sampling of [[analog]] waveforms, such as [[sound]] waves.  When the digital sample is converted back to an analog waveform - such as when a [[CD]] is played - the player will emit the lowest '''alias''' waveform, which might not be the sound actually recorded.

==The Problem==

==The Problem==

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 &lt; 1/2 f_s</tt>, then  f_s is, by definition, greater than two times the sample's frequency.  If <tt>g &gt; 1/2 f_s</tt>, then <tt>f_s-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_s.

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 &lt; 1/2 f_s</tt>, then  f_s is, by definition, greater than two times the sample's frequency.  If <tt>g &gt; 1/2 f_s</tt>, then <tt>f_s-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_s.

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.