Rounding samples to finite levels introduces quantisation noise.
Quantisation maps continuous amplitudes to 2ᴺ discrete levels, introducing error with uniform distribution of variance Δ²/12. SQNR≈6.02N+1.76 dB for a full-scale sine. Non-uniform (μ-law, A-law) quantisers suit speech; dithering decorrelates error.
16-bit audio has about 98 dB dynamic range.
Quantisation adds rounding noise when continuous values are stored in finite digits, which limits the accuracy of every digital measurement.
Rounding samples to finite levels introduces quantisation noise.
Quantisation adds rounding noise when continuous values are stored in finite digits, which limits the accuracy of every digital measurement.
The error from rounding each sample to the nearest level, which for an ideal converter has a power set by the step size.
About six decibels more signal-to-quantisation-noise ratio, so the resolution improves steadily with bit depth.
Typical applications include estimating the noise floor of a 12-bit ADC in a measurement system, choosing the number of bits for an audio recording and deciding whether a sensor reading needs dithering to show small changes.
Study "Aliasing" first (topic 24 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
Step size Δ=range/2ᴺ. Clipping. Noise shaping.
16-bit audio has about 98 dB dynamic range.
The next topic is "Discrete-time Fourier transform", which builds directly on this one.
It is classed as Beginner in Signals, Control & Comms (topic 25 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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