cycles. Noise Distributions Rectangular probability density function (RPDF) dither noise has a uniform distribution; any value in the specified range has the same probability of occurring. Triangular probability density function (TPDF) dither noise has a triangular distribution; values in the center of the range have a higher probability of occurring. Triangular distribution can be achieved by adding two independent RPDF sources. Gaussian PDF has a normal distribution. The relationship of probabilities of results follows a bell-shaped, or Gaussian curve, typical of dither generated by analog sources such as microphone preamplifiers. If the bit depth of a recording is sufficiently great, that preamplifier noise will be sufficient to dither the recording. Noise shaping is a filtering process that shapes the spectral energy of quantization error, typically to either de-emphasize frequencies to which the ear is most sensitive or separate the signal and noise bands completely. If dither is used, its final spectrum depends on whether it is added inside or outside the feedback loop of the noise shaper. If inside, the dither is treated as part of the error signal and shaped along with actual quantization error. If outside, the dither is treated as part of the original signal and linearises quantization without being shaped itself. In this case, the final noise floor is the sum of the flat dither spectrum and the shaped quantization noise. While real-world noise shaping usually includes in-loop dithering, it is also possible to use it without adding dither at all, in which case quantization error is evident at low signal levels. Colored dither is sometimes mentioned as dither that has been filtered to be different from white noise. Noise shaping is one such application. Which noise distribution to use If the signal being dithered is to undergo further processing, then it should be processed with a triangular-type dither that has an amplitude of two quantization steps so that the dither values computed range from, for example, −1 to +1, or 0 to 2. This is the lowest power ideal dither, in that it does not introduce noise modulation (which would manifest as a constant noise floor), and eliminates the harmonic distortion from quantization. If a colored dither is used instead at these intermediate processing stages, then frequency content may bleed into other frequency ranges that are more noticeable and become distractingly audible. If the signal being dithered is to undergo no further processing – if