tags: music mus-407 electroacoustic computer digital audio sampling bit-depth dynamic-range quantization

Bit Depth

Bit depth (or sample width) in a [digital audio] encoding system determines the number of [bit]s used to represent each [sample].

• i.e. the number of available resolution points to which a measured analog value can be approximated
• 1 [byte] = 8 bits

Number of resolution points = $2^{\text{bit depth}}$

• 1-bit system; 2 resolution points
• 2-bit system; 4 resolution points
• 8-bit system; 256 resolution points
• 16-bit system; 65536 resolution points (1 byte per sample)
• 32-bit system; a lot of resolution points (4 bytes per sample)

Consider the analog-to-digital conversion process in a 3-bit system:

The [amplitude] of each sample is quantized to a particular bit and encoded into binary. Through [PCM], we then encode the binary into a modulated pulse wave.

Bit depth determines the maximum [dynamic range] of a digital audio signal, resulting in the relative amount of [dB]s available.

• 16-bits gives us 96 dB to work
• 24-bits gives us 120-something dB
• Our pain threshold goes up to 120-something dB, so we don't need to raise the bit depth past something like 16-bits.

dynamic range (dB) ~= 6 x bit depth, e.g. an 8-bit system provides 48 dB of dynamic range

• signals at or below -48 dBFS will be unresolvable from the [noise floor]

Reducing the bit depth, and therefore dynamic range, does not reduce the number of samples taken (the sample rate). We can still represent high [frequency] content, but reducing the bit depth reduces the dynamic range at which we can represent the audio content.