Documentation sections

FFT Bin Resolution & Spectral Analysis Calculator

POSThttps://rftools.io/api/py/v1/calculate

Slug fft-bin-resolution. Calculate FFT frequency bin resolution, Nyquist range, time record length, and scalloping loss. Design spectral analysis parameters for DSP systems. Free, instant results.

Inputs

Send every one of these in inputs, in the units shown. Most are required: a call without one is refused (400) and costs nothing; one the calculator can do without takes the default shown. An input outside its range is still computed and flagged in the provenance.

Inputs of fft-bin-resolution
Name	Unit	Range	Default	Description
sampleRatenumber	kHz	at least 0.001	44.1	Sample Rate
fftSizenumber	points	at least 8	1024	Number of FFT points (power of 2 recommended)
windowTypenumber	none	0 … 2	1	Window FunctionOne of: 0 Rectangular · 1 Hann · 2 Blackman
toneFreqnumber	Hz	at least 0	1000	A tone to place on the bins: how far it falls from a bin centre sets how low the FFT reads it
sidebandSpacingnumber	Hz	at least 0.001	100	The spacing of the neighbours to separate from the tone, at f₀ ± Δ, ± 2Δ and ± 3Δ: modulation sidebands, motor slip sidebands, mains hum

Outputs

Returned in values, by key. A value that is unbounded or undefined is null.

Outputs of fft-bin-resolution
Field	Unit	Description
binResolutionheadline	Hz	Frequency Bin Resolution
frequencyRange	kHz	Frequency Range (Nyquist)
timeRecord	ms	Time Record Length
noiseFloor	dB	Noise floor improvement from coherent FFT integration
scalloping	dB	Scalloping Loss
toneBin	bins	Where the tone falls on the bins: its frequency over the bin width; a whole number is a tone on a bin centre
toneLevelError	dB	How far below the tone's true level the nearest bin reads it, from the window's response at the tone's offset from that bin; at half a bin it is the scalloping loss
resolutionBandwidth	Hz	The window's 6 dB bandwidth: two tones of equal strength closer than this show one peak (Harris 1978); a weaker neighbour needs more
sidebandsUnresolved	none	Of the neighbours at f₀ ± Δ, ± 2Δ and ± 3Δ inside the FFT's range, those within the 6 dB bandwidth of the tone: they merge with it into one peak

Calling it

Calculate: one call, the request and response in full, and its errors.
Batch: this calculator with others, or a sweep, in one request.
Solve for a target: the value of one input that brings an output to a target.

curl -X POST https://rftools.io/api/py/v1/calculate \
  -H "X-API-Key: $RFTOOLS_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "slug": "fft-bin-resolution",
    "inputs": {
      "sampleRate": 44.1,
      "fftSize": 1024,
      "windowType": 1,
      "toneFreq": 1000,
      "sidebandSpacing": 100
    }
  }'

import rftools

client = rftools.Client()  # reads RFTOOLS_API_KEY, or the key `rftools login` saved

result = client.calculate("fft-bin-resolution", {
    "sampleRate": 44.1,
    "fftSize": 1024,
    "windowType": 1,
    "toneFreq": 1000,
    "sidebandSpacing": 100,
})
print(result.values)
print(result.warnings, result.provenance.formula_ref)

const response = await fetch("https://rftools.io/api/py/v1/calculate", {
  method: "POST",
  headers: {
    "X-API-Key": process.env.RFTOOLS_API_KEY,
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
    "slug": "fft-bin-resolution",
    "inputs": {
      "sampleRate": 44.1,
      "fftSize": 1024,
      "windowType": 1,
      "toneFreq": 1000,
      "sidebandSpacing": 100
    }
  }),
});
console.log(response.status, await response.json());

package main

import (
	"bytes"
	"fmt"
	"io"
	"net/http"
	"os"
)

func main() {
	body := []byte(`{
	  "slug": "fft-bin-resolution",
	  "inputs": {
	    "sampleRate": 44.1,
	    "fftSize": 1024,
	    "windowType": 1,
	    "toneFreq": 1000,
	    "sidebandSpacing": 100
	  }
	}`)
	req, err := http.NewRequest("POST", "https://rftools.io/api/py/v1/calculate", bytes.NewReader(body))
	if err != nil {
		panic(err)
	}
	req.Header.Set("X-API-Key", os.Getenv("RFTOOLS_API_KEY"))
	req.Header.Set("Content-Type", "application/json")
	res, err := http.DefaultClient.Do(req)
	if err != nil {
		panic(err)
	}
	defer res.Body.Close()
	out, _ := io.ReadAll(res.Body)
	fmt.Println(res.Status, string(out))
}

application/json

{
  "slug": "fft-bin-resolution",
  "values": {
    "binResolution": 43.06640625,
    "frequencyRange": 22.05,
    "timeRecord": 23.219954648526077,
    "noiseFloor": -27.09269960975831,
    "scalloping": 1.42,
    "toneBin": 23.219954648526077,
    "toneLevelError": 0.27185918276928983,
    "resolutionBandwidth": 86.1328125,
    "sidebandsUnresolved": 0
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:fft-bin-resolution",
    "version": "api@3f2c1a9b04de",
    "formulaRef": null,
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "sampleRate": {
          "min": 0.001,
          "max": null,
          "unit": "kHz"
        },
        "fftSize": {
          "min": 8,
          "max": null,
          "unit": "points"
        },
        "windowType": {
          "min": 0,
          "max": 2,
          "unit": ""
        },
        "toneFreq": {
          "min": 0,
          "max": null,
          "unit": "Hz"
        },
        "sidebandSpacing": {
          "min": 0.001,
          "max": null,
          "unit": "Hz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "sampleRate": 44.1,
      "fftSize": 1024,
      "windowType": 1,
      "toneFreq": 1000,
      "sidebandSpacing": 100
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "sampleRate"
      ],
      "msg": "Input should be a valid number, unable to parse string as a number",
      "input": "abc"
    }
  ]
}

An input sent as text. Nothing was counted.

{
  "detail": "More than 120 requests in 60 seconds from this address.",
  "errorKind": "rate_limited",
  "limit": 120,
  "windowSeconds": 60,
  "upgradeUrl": "https://rftools.io/pricing/"
}

Too many requests in a minute, with Retry-After.

Same inputs on the calculator pageFFT Bin Resolution & Spectral Analysis Calculator, at these values