FFT Noise Floor
Floor = SNR + 10·log10(M/2) below FS
Quick answer
This calculator solves Noise floor = SNR + 10 × log10(M/2) (dB below full scale) for Noise Floor Below FS. With Converter SNR 44 dB, FFT Length 0.5, the result is 37.98 dB. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| NF | Noise Floor Below FS | dB | dB |
| SNR | Converter SNR | dB | dB |
| M | FFT Length | — | — |
Step by step
- 1. What you know: Converter SNR 44 dB, FFT Length 0.5
- 2. The relation: Noise floor = SNR + 10 × log10(M/2) (dB below full scale)
- 3. Substitute: SNR = 44 dB, M = 0.5
- 4. Result: Noise Floor Below FS = 37.98 dB
Worked examples
Minimum range
Given: Converter SNR 0.66 dB, FFT Length 0.025
Result: Noise Floor Below FS = -18.37 dB
Low range
Given: Converter SNR 6.6 dB, FFT Length 0.25
Result: Noise Floor Below FS = -2.431 dB
Typical
Given: Converter SNR 44 dB, FFT Length 0.5
Result: Noise Floor Below FS = 37.98 dB
High range
Given: Converter SNR 132 dB, FFT Length 0.8
Result: Noise Floor Below FS = 128 dB
Maximum range
Given: Converter SNR 1320 dB, FFT Length 8
Result: Noise Floor Below FS = 1326 dB
Solving for each variable
Solve for Noise Floor Below FS
Converter SNR 0.66 dB, FFT Length 0.025 → -18.37 dB
Solve for Converter SNR
Noise Floor Below FS 0.3 dB, FFT Length 0.025 → 19.33 dB
Solve for FFT Length
Noise Floor Below FS 0.3 dB, Converter SNR 0.66 dB → 1.841
How Noise Floor Below FS changes with Converter SNR
| Converter SNR (input) | Noise Floor Below FS (result) |
|---|---|
| 4.4 dB | -1.621 dB |
| 11 dB | 4.979 dB |
| 22 dB | 15.98 dB |
| 33 dB | 26.98 dB |
| 44 dB | 37.98 dB |
| 66 dB | 59.98 dB |
| 88 dB | 81.98 dB |
| 176 dB | 170 dB |
| 308 dB | 302 dB |
| 440 dB | 434 dB |
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<p><a href="https://vbatpower.com/formulas/fft-noise-floor/">FFT Noise Floor</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate FFT Noise Floor?
Use Noise floor = SNR + 10 × log10(M/2) (dB below full scale). With Converter SNR 44 dB, FFT Length 0.5, Noise Floor Below FS works out to 37.98 dB.
What is the formula for FFT Noise Floor?
The formula is 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.
How do you find Converter SNR when you know the other values?
Rearrange for Converter SNR: with Noise Floor Below FS 0.3 dB, FFT Length 0.025, Converter SNR is 19.33 dB.
How do you find FFT Length when you know the other values?
Rearrange for FFT Length: with Noise Floor Below FS 0.3 dB, Converter SNR 0.66 dB, FFT Length is 1.841.
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