Editing Signal-to-noise ratio (section)

===Fixed point===
{{See also|Fixed-point arithmetic}}

For ''n''-bit integers with equal distance between quantization levels ([[quantization (signal processing)|uniform quantization]]) the [[dynamic range]] (DR) is also determined.

Assuming a uniform distribution of input signal values, the quantization noise is a uniformly distributed random signal with a peak-to-peak amplitude of one quantization level, making the amplitude ratio 2<sup>''n''</sup>/1. The formula is then:
:<math>
\mathrm{DR_{dB}} = \mathrm{SNR_{dB}} = 20 \log_{10}(2^n) \approx 6.02 \cdot n
</math>

This relationship is the origin of statements like "[[16-bit audio]] has a dynamic range of 96&nbsp;dB". Each extra quantization bit increases the dynamic range by roughly 6&nbsp;dB.

Assuming a [[full-scale]] [[sine wave]] signal (that is, the quantizer is designed such that it has the same minimum and maximum values as the input signal), the quantization noise approximates a [[sawtooth wave]] with peak-to-peak amplitude of one quantization level<ref name="maxim 728">[http://www.maxim-ic.com/appnotes.cfm/appnote_number/728 Defining and Testing Dynamic Parameters in High-Speed ADCs] — [[Maxim Integrated Products]] Application note 728</ref> and uniform distribution. In this case, the SNR is approximately
:<math>
\mathrm{SNR_{dB}} \approx 20 \log_{10} (2^n {\textstyle\sqrt {3/2}}) \approx 6.02 \cdot n + 1.761
</math>