Documentation sections

Oversampling & Noise Shaping SNR Calculator

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

Slug oversampling-snr. Calculate SNR improvement from oversampling and noise shaping for sigma-delta ADCs. Determine effective bits gained from higher OSR. 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 oversampling-snr
Name	Unit	Range	Default	Description
bitsnumber	bits	1 … 24	12	Underlying quantizer resolution
oversamplingRationumber	none	at least 1	64	Ratio of sampling rate to Nyquist rate
noiseShapingOrdernumber	none	0 … 5	1	Order of the noise-shaping loop; 0 is plain oversampling with no shaping
signalBandwidthnumber	Hz	at least 0.001	24000	The band the converter delivers, half its output rate: 24 kHz for 48 kHz audio. The modulator runs at 2·OSR·f_B

Outputs

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

Outputs of oversampling-snr
Field	Unit	Description
baseSnr	dB	Base SNR (Nyquist)
oversampledSnrheadline	dB	Oversampled SNR
effectiveBits	bits	Effective Bits
snrImprovement	dB	SNR Improvement
modulatorRate	Hz	The rate the modulator samples at, 2·OSR·f_B
outOfBandNoise	dB	The shaped quantization noise between f_B and f_s/2 against the noise left inside the band: what the decimation filter must remove before it can fold back
foldBands	none	Decimating to f_s/OSR folds every band 2·f_B wide around a multiple of the output rate onto the signal band, OSR/2 of them: the decimation filter must reject each (the plan draws at most 1024)

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": "oversampling-snr",
    "inputs": {
      "bits": 12,
      "oversamplingRatio": 64,
      "noiseShapingOrder": 1,
      "signalBandwidth": 24000
    }
  }'

import rftools

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

result = client.calculate("oversampling-snr", {
    "bits": 12,
    "oversamplingRatio": 64,
    "noiseShapingOrder": 1,
    "signalBandwidth": 24000,
})
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": "oversampling-snr",
    "inputs": {
      "bits": 12,
      "oversamplingRatio": 64,
      "noiseShapingOrder": 1,
      "signalBandwidth": 24000
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "oversampling-snr",
	  "inputs": {
	    "bits": 12,
	    "oversamplingRatio": 64,
	    "noiseShapingOrder": 1,
	    "signalBandwidth": 24000
	  }
	}`)
	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": "oversampling-snr",
  "values": {
    "baseSnr": 74.0081115499123,
    "oversampledSnr": 123.02172586274287,
    "effectiveBits": 20.14098512088826,
    "snrImprovement": 49.01361431283057,
    "modulatorRate": 3072000,
    "outOfBandNoise": 52.0244102542922,
    "foldBands": 32
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:oversampling-snr",
    "version": "api@3f2c1a9b04de",
    "formulaRef": null,
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "bits": {
          "min": 1,
          "max": 24,
          "unit": "bits"
        },
        "oversamplingRatio": {
          "min": 1,
          "max": null,
          "unit": ""
        },
        "noiseShapingOrder": {
          "min": 0,
          "max": 5,
          "unit": ""
        },
        "signalBandwidth": {
          "min": 0.001,
          "max": null,
          "unit": "Hz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "bits": 12,
      "oversamplingRatio": 64,
      "noiseShapingOrder": 1,
      "signalBandwidth": 24000
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "bits"
      ],
      "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 pageOversampling & Noise Shaping SNR Calculator, at these values