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==Limitations==
The [[Nyquist–Shannon sampling theorem]] shows PCM devices can operate without introducing distortions within their designed frequency bands if they provide a sampling frequency at least twice that of the highest frequency contained in the input signal. For example, in [[telephony]], the usable [[voice frequency]] band ranges from approximately 300 to 3400 [[Hz]]
Regardless, there are potential sources of impairment implicit in any PCM system:
* Choosing a discrete value that is near but not exactly at the analog signal level for each sample leads to [[quantization error]]. When [[dither]]ing is used to compensate for this, it introduces additional noise.<ref group=note>Quantization error swings between -''q''/2 and ''q''/2. In the ideal case (with a fully linear ADC and signal level >> ''q'') it is [[uniform distribution (continuous)|uniformly distributed]] over this interval, with zero mean and variance of ''q''<sup>2</sup>/12.</ref>
* Between samples no measurement of the signal is made; the sampling theorem guarantees non-ambiguous representation and recovery of the signal only if it has no energy at frequency ''f<sub>s</sub>''/2 or higher (one half the sampling frequency, known as the [[Nyquist frequency]]); higher frequencies will not be correctly represented or recovered and add aliasing distortion to the signal below the Nyquist frequency.
* As samples are dependent on time, an accurate clock is required for accurate reproduction. If either the encoding or decoding clock is not stable, these imperfections will directly affect the output quality of the device.<ref group=note>A slight difference between the encoding and decoding clock frequencies is not generally a major concern; a small constant error is not noticeable. Clock error does become a major issue if the clock contains significant [[jitter]], however.</ref>
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