Fast frequency detection using the Goertzel algorithm

The Goertzel algorithm is a fast alternative to the Fast Fourier Transform that is optimized for detecting the presence of a single frequency in a buffer of signal samples (radio waves, sound, light).

Let's detect a sine wave with a frequency of 2 kHz:

var goertzel = require('goertzel')

var detect = goertzel({
  targetFrequency: 2000,  // 2 kHz
  sampleRate: 10000,      // 1000 samples per second
  samplesPerFrame: 100    // 100 samples per buffer
})

// Generates a sine wave at some Hz and time (ms)
function sin (hz, t) {
  return Math.sin(Math.PI * 2 * t * hz)
}

// Populate a buffer with a sine wave at 2 kHz for 100 samples
var sin2 = []
for (var i = 0; i < 100; i++) {
  var v = sin(2, i / 100)
  sin2.push(v)
}

// Populate a buffer with a sine wave at 19 kHz for 100 samples
var sin19 = []
for (var i = 0; i < 100; i++) {
  var v = sin(19, i / 100)
  sin19.push(v)
}

console.log(detect(sin19))
console.log(detect(sin2))

This will output

false
true

var goertzel = require('goertzel')

Returns a function set to detect a single frequency.

opts is mandatory, and has some required and optional parameters:

• opts.targetFrequency (required) - the frequency, in Hertz, to detect.
• opts.sampleRate (required) - how many samples are taken per second. For best results, this should be at least twice the Nyquist frequency. 2.5x works well.
• opts.samplesPerFrame (required) - how many samples will be included in each frame to be tested.
• opts.threshold (optional) - The Goertzel algorithm returns a relative magnitude of how well the samples match the targetFrequency. Set this to control the threshold. In general, the default value can be used safely.

Given a buffer of floating point audio samples (-1..1), returns a boolean: true if the targetFrequency is present in the samples, and false otherwise.

With npm installed, run

$ npm install goertzel

An understanding of the algorithm was gleaned from https://en.wikipedia.org/wiki/Goertzel_algorithm and http://www.embedded.com/design/configurable-systems/4024443/The-Goertzel-Algorithm.

• noffle/mic-stream

MIT