Audio bit depth
In basic implementations, variations in bit depth primarily affect the noise level from quantization error—thus the signal-to-noise ratio (SNR) and dynamic range.
However, techniques such as dithering, noise shaping, and oversampling can mitigate these effects without changing the bit depth.
Integer PCM audio data is typically stored as signed numbers in two's complement format.
[9] The bit depth limits the signal-to-noise ratio (SNR) of the reconstructed signal to a maximum level determined by quantization error.
For example, the Motorola 56000 DSP chip uses 24-bit multipliers and 56-bit accumulators to perform multiply-accumulate operations on two 24-bit samples without overflow or truncation.
[24] On devices that do not support large accumulators, fixed-point results may be truncated, reducing precision.
Errors compound through multiple stages of DSP at a rate that depends on the operations being performed.
For uncorrelated processing steps on audio data without a DC offset, errors are assumed to be random with zero means.
[23] High levels of precision are also necessary in recursive algorithms, such as infinite impulse response (IIR) filters.
[23] The noise introduced by quantization error, including rounding errors and loss of precision introduced during audio processing, can be mitigated by adding a small amount of random noise, called dither, to the signal before quantizing.
Dithering eliminates non-linear quantization error behavior, giving very low distortion, but at the expense of a slightly raised noise floor.
Recommended dither for 16-bit digital audio measured using ITU-R 468 noise weighting is about 66 dB below alignment level, or 84 dB below digital full scale, which is comparable to the microphone and room noise level, and hence of little consequence in 16-bit audio.
The perceived dynamic range of 16-bit audio can be 120 dB or more with noise-shaped dither, taking advantage of the frequency response of the human ear.
[30] The use of techniques such as oversampling and noise shaping can further extend the dynamic range of sampled audio by moving quantization error out of the frequency band of interest.
If the signal's maximum level is lower than that allowed by the bit depth, the recording has headroom.
Using higher bit depths during studio recording can make headroom available while maintaining the same dynamic range.
Oversampling is an alternative method to increase the dynamic range of PCM audio without changing the number of bits per sample.
Philips had implemented 4× oversampling with first order noise shaping which theoretically realized the full 96 dB dynamic range of the CD format.
[35] For example, for a 20 kHz analog audio sampled at 4× oversampling with second-order noise shaping, the dynamic range is increased by 30 dB.
