Averaging SNR Improvement

Formula

Description

Averaging N independent measurements of a signal improves the signal-to-noise ratio because the coherent signal adds linearly while uncorrelated noise adds in quadrature (RMS). The SNR improvement follows a square-root law: averaging 4 samples doubles the SNR (3 dB gain), averaging 16 samples quadruples it (6 dB), and averaging 100 samples gives a 10x improvement (10 dB). This technique is widely used in oscilloscopes, spectrum analyzers, ADC oversampling, and any measurement system where trading time for accuracy is acceptable.

Variables

• SNR_gain — SNR improvement in decibels (dB)
• N — Number of independent averages

Practical Notes

Averaging only works for uncorrelated (white) noise. Correlated noise or interference at the signal frequency does not average out. For real-time systems, exponential moving average provides continuous noise reduction with adjustable time constant. In ADCs, oversampling by 4x followed by decimation gains 1 bit (6 dB) of effective resolution.