Also known as: quantisation, amplitude quantization
Quantization is the step in digitising a signal where each sampled amplitude is rounded to the nearest value in a finite set of levels.1 Where sampling discretises a signal in time, quantization discretises it in amplitude: a converter with N bits has 2N levels, and every real measurement is snapped to whichever level is closest. The small rounding error left behind is quantization noise, and it sets the noise floor of an ideal converter.
How it works
Divide the converter’s full-scale range into 2N equal steps. The width of one step is the least significant bit (LSB). Rounding to the nearest level means the error on any sample lies between −½ and +½ LSB. For a busy signal that exercises many levels, that error behaves like additive random noise, uniformly distributed over one LSB, with power equal to Δ²/12 (Δ being the step size). This gives the standard result for an ideal uniform quantizer:
SQNR ≈ 6.02·N + 1.76 dB
where SQNR is the signal-to-quantization-noise ratio for a full-scale sine wave. The practical takeaway is the 6 dB-per-bit rule: each additional bit halves the step size, cutting quantization noise power by a factor of four and adding roughly 6 dB of dynamic range. An 8-bit converter reaches about 50 dB, a 12-bit about 74 dB, a 16-bit about 98 dB — before real-world imperfections erode it.
In practice
The clean 6-dB formula assumes the error is random and uncorrelated with the signal. For low-level or slowly varying signals that only cross a few levels, that assumption breaks: the error becomes a correlated distortion, producing spurious tones instead of smooth noise. Dither — a tiny amount of added noise before quantization — decorrelates the error, trading those ugly tones for a slightly higher but benign noise floor. Real converters also fall short of the ideal: differential and integral nonlinearity, aperture jitter, and thermal noise mean the effective resolution, captured by the ENOB figure, is always below the nominal bit count.
Quantization is measured relative to full scale, so a signal’s headroom is expressed in dBFS; the same discretisation happens in reverse in a digital-to-analog converter.
Relevance to SDR
An SDR’s bit depth sets how far a weak signal can sit below a strong one before the weak one disappears into quantization noise — the core of receiver dynamic range. It is why an 8-bit RTL-SDR struggles when a strong nearby transmitter shares the passband, while a 12- or 16-bit receiver has room to spare, and why front-end gain must be staged to fill the ADC without clipping. In a wideband trunking capture, quantization noise across the whole span competes with every channel at once, so bit depth directly affects how weak a control channel can be and still decode.
GopherTrunk consumes already-quantized IQ samples, so it inherits whatever quantization noise the capture device imposed; its DSP cannot recover detail lost below the LSB, which is why capture gain staging matters upstream of the decoder.
Sources
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Quantization (signal processing) — Wikipedia, on rounding to discrete levels and the resulting quantization error. ↩