Any time a signal is quantized, error is introduced. Although dither is most often considered when performing an A-to-D conversion, error occurs regardless of whether or not the conversion is cross domain.
The error is highly correlated with the signal, so when the signal is small, the correlation renders it highly audible. Even worse, at very low signal levels the signal will drop out completely because its excursions are smaller than one quantization step.
For high resolution ADCs, this is not actually a problem because the noise floor of the analog front ends is much greater than a quantization step. These systems are therefore self-dithering.
However, for digital wordlength reduction (e.g. reducing a signal from 24-bit studio master to 16-bit CD), and for low resolution ADCs, quantization introduces unacceptable distortion.
To counteract this error, dither is added before quantization.
Dither is a noise signal, usually generated pseudo-randomly. The ideal dither adds the minimum amount of noise power while achieving the goals of dither. In audio, these goals are accepted to be (a) zero harmonic distortion from quantization and (b) no noise modulation. The lowest power dither which achieves this is triangular probability distribution function (TPDF) dither with an excursion of +/- 1 LSB.
Several benefits result from the addition of TPDF dither before quantization:
Rectangular dither (RPDF) is non-ideal because although it eliminates distortion, it suffers from audible noise modulation.
Shaped dither, or wordlength reducers embedded in psychoacoustic feedback networks, can achieve better performance than TPDF dither in that the noise floor power spectrum can be shaped for minimum audibility. The actual noise power is not reduced over TPDF dither, just its audibility. This is used in some commercial CDs to improve performance.
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