What is the formula for FFT Noise Floor?

The FFT Noise Floor formula is Noise floor = SNR + 10 × log10(M/2) (dB below full scale), where Floor—FFT noise floor (dB below full scale); SNR—Converter signal-to-noise ratio (dB); M—FFT length (points).

What does Floor mean in the FFT Noise Floor formula?

Floor is FFT noise floor (dB below full scale).

FFT Noise Floor

Q: How do you calculate FFT Noise Floor?

Use the formula Noise floor = SNR + 10 × log10(M/2) (dB below full scale). In an FFT plot the average noise floor sits below the full-scale reference by the converter’s SNR plus the processing gain of the transform. Enter the values you know in the calculator above and it solves for the remaining variable.

Floor = SNR + 10·log10(M/2) below FS

Calculator

Noise Floor Below FS

Converter SNR

FFT Length

Result

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Formula

Noise floor = SNR + 10 × log10(M/2) (dB below full scale)

Description

In an FFT plot the average noise floor sits below the full-scale reference by the converter’s SNR plus the processing gain of the transform. This is why spurs much smaller than the noise power can still be measured: they rise above the processing-gain-lowered floor. Knowing the floor lets you set the FFT length needed to resolve a spur of a given size.

Variables

Floor — FFT noise floor (dB below full scale)
SNR — Converter signal-to-noise ratio (dB)
M — FFT length (points)

Practical Notes

A 65 dB SNR converter with a 8192-point FFT shows a noise floor about 101 dB below full scale. Spurs above that floor are measurable even though they are below the total noise.

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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