Digital Sound & Music: Concepts, Applications, & Science, Chapter 5, last updated 6/25/2013

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Figure 5.39 Triangular probability density function

Audio processing programs like Adobe Audition or Sound Forge offer a variety of

probability functions for noise shaping, as shown in Figure 5.40. The rectangular probability

density function gives equal probability for all numbers within a given range. The Gaussian

function weighs the probabilities according to a Gaussian rather than a triangular shape, so it

would look like Figure 5.39 except more bell-shaped. This creates noise that is more like

common environmental noise, like tape hiss.

Figure 5.40 Probability functions for noise shaping

Requantization without dithering, with dithering, and with dithering and noise shaping

are compared in Figure 5.41. A 16-bit audio file has been requantized to 4 bits (an unlikely

scenario, but it makes the point). From these graphs, it may look like noise shaping adds

additional noise. In fact, the reason the noise graph looks more dense when noise shaping is

added is that the frequency components are higher.