Decimation ENOB Gain

Formula

Description

Oversampling followed by decimation (averaging and downsampling) increases the effective number of bits of an ADC. Each quadrupling of the sample rate gains one additional bit of resolution. This technique spreads the quantization noise across a wider bandwidth, then the decimation filter removes the out-of-band noise, leaving a cleaner signal at the original Nyquist rate. Sigma-delta ADCs exploit this principle with very high oversampling ratios (64x to 256x) combined with noise shaping to achieve 24-bit resolution from a simple 1-bit comparator.

Variables

• ENOB_gain — Additional effective bits of resolution
• N — Oversampling ratio (sampling rate / Nyquist rate)

Practical Notes

To gain 1 bit, oversample 4x. To gain 2 bits, oversample 16x. To gain 4 bits, oversample 256x. This assumes white noise and a proper decimation filter (not just averaging). Sigma-delta ADCs add noise shaping which pushes more quantization noise out of band, allowing much greater ENOB gain per octave of oversampling.