What is the formula for FFT Processing Gain?

The FFT Processing Gain formula is PG = 10 × log10(M / 2), where PG—FFT processing gain (dB); M—Number of FFT points.

What does PG mean in the FFT Processing Gain formula?

PG is FFT processing gain (dB).

FFT Processing Gain

Q: How do you calculate FFT Processing Gain?

Use the formula PG = 10 × log10(M / 2). An FFT spreads broadband noise across all its bins while concentrating a coherent tone into one bin, so the noise floor in the spectrum sits below the converter’s full SNR by the processing gain. Enter the values you know in the calculator above and it solves for the remaining variable.

PG = 10 · log10(M / 2)

Calculator

Processing Gain

FFT Length

Result

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Formula

PG = 10 × log10(M / 2)

Description

An FFT spreads broadband noise across all its bins while concentrating a coherent tone into one bin, so the noise floor in the spectrum sits below the converter’s full SNR by the processing gain. A longer transform gives more processing gain and a lower displayed noise floor, letting small spurs and tones be seen far below the total noise power.

Variables

PG — FFT processing gain (dB)
M — Number of FFT points

Practical Notes

Doubling the FFT length adds 3 dB of processing gain. The plotted noise floor is the SNR plus PG below full scale—do not mistake this low floor for the converter’s actual SNR.

Related Concepts

All Signal Processing formulas →

FFT Bin Resolution Averaging SNR Improvement Decimation ENOB Gain FFT Frequency Bin Decimation Resolution Gain FFT Processing Gain FFT Noise Floor

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