FFT Processing Gain

PG = 10 · log10(M / 2)

Quick answer

This calculator solves PG = 10 × log10(M / 2) for Processing Gain. With FFT Length 0.5, the result is -6.021 dB. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Processing Gain (dB)
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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.

Symbols and units

Symbol Meaning Default unit Accepted units
PG Processing Gain dB dB
M FFT Length — —

Step by step

  1. 1. What you know: FFT Length 0.5
  2. 2. The relation: PG = 10 × log10(M / 2)
  3. 3. Substitute: M = 0.5
  4. 4. Result: Processing Gain = -6.021 dB

Worked examples

Minimum range

Given: FFT Length 0.025

Result: Processing Gain = -19.03 dB

Low range

Given: FFT Length 0.25

Result: Processing Gain = -9.031 dB

Typical

Given: FFT Length 0.5

Result: Processing Gain = -6.021 dB

High range

Given: FFT Length 0.8

Result: Processing Gain = -3.979 dB

Maximum range

Given: FFT Length 8

Result: Processing Gain = 6.021 dB

Solving for each variable

Solve for Processing Gain

FFT Length 0.025 → -19.03 dB

Solve for FFT Length

Processing Gain 0.3 dB → 2.143

How Processing Gain changes with FFT Length

FFT Length (input) Processing Gain (result)
0.05 -16.02 dB
0.125 -12.04 dB
0.25 -9.031 dB
0.375 -7.27 dB
0.5 -6.021 dB
0.75 -4.26 dB
1 -3.01 dB
3.5 2.43 dB
5 3.979 dB

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Frequently asked questions

How do you calculate FFT Processing Gain?

Use PG = 10 × log10(M / 2). With FFT Length 0.5, Processing Gain works out to -6.021 dB.

What is the formula for FFT Processing Gain?

The formula is 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.

How do you find FFT Length when you know the other values?

Rearrange for FFT Length: with Processing Gain 0.3 dB, FFT Length is 2.143.

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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