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