@qgustavor/stream-audio-fingerprint/src/lib/fft.mts

Audio landmark fingerprinting as a JavaScript module

// Original from: https://www.nayuki.io/page/free-small-fft-in-multiple-languages
// Modified by Chris Cannam: https://code.soundsoftware.ac.uk/projects/js-dsp-test/repository/entry/fft/nayuki-obj/fft.js

/*
 * Free FFT and convolution (JavaScript)
 *
 * Copyright (c) 2014 Project Nayuki
 * http://www.nayuki.io/page/free-small-fft-in-multiple-languages
 *
 * (MIT License)
 * Permission is hereby granted, free of charge, to any person obtaining a copy of
 * this software and associated documentation files (the "Software"), to deal in
 * the Software without restriction, including without limitation the rights to
 * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
 * the Software, and to permit persons to whom the Software is furnished to do so,
 * subject to the following conditions:
 * - The above copyright notice and this permission notice shall be included in
 *   all copies or substantial portions of the Software.
 * - The Software is provided "as is", without warranty of any kind, express or
 *   implied, including but not limited to the warranties of merchantability,
 *   fitness for a particular purpose and noninfringement. In no event shall the
 *   authors or copyright holders be liable for any claim, damages or other
 *   liability, whether in an action of contract, tort or otherwise, arising from,
 *   out of or in connection with the Software or the use or other dealings in the
 *   Software.
 *
 * Original slightly restructured by Chris Cannam, cannam@all-day-breakfast.com
 * Restructured again to use the Typescript variant by Lucas Polito, https://github.com/lpolito
 * Typescript from: https://www.nayuki.io/res/free-small-fft-in-multiple-languages/fft.ts
 */

/*
 * Construct an object for calculating the discrete Fourier transform (DFT) of size n, where n is a power of 2.
 */
class FFTNayuki {
  private readonly n: number
  private readonly levels: number
  private readonly cosTable: number[]
  private readonly sinTable: number[]
  public spectrum: number[]
  public peakBand = 0
  public peak = 0

  /**
    * @param n Buffer size.
    */
  constructor (n: number) {
    this.n = n

    this.levels = -1
    for (let i = 0; i < 32; i++) {
      if (1 << i === n) {
        this.levels = i // Equal to log2(n)
      }
    }
    if (this.levels === -1) {
      throw Error('Length is not a power of 2')
    }

    // Trigonometric tables
    this.cosTable = new Array(n / 2)
    this.sinTable = new Array(n / 2)
    for (let i = 0; i < n / 2; i++) {
      this.cosTable[i] = Math.cos(2 * Math.PI * i / n)
      this.sinTable[i] = Math.sin(2 * Math.PI * i / n)
    }

    this.spectrum = new Array(n / 4)
  }

  /*
   * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
   * The vector's length must be equal to the size n that was passed to the object constructor, and this must be a power of 2. Uses the Cooley-Tukey decimation-in-time radix-2 algorithm.
   */
  public forward (real: number[]|Float64Array, imag: number[]|Float64Array): void {
    // Bit-reversed addressing permutation
    for (let i = 0; i < this.n; i++) {
      const j: number = reverseBits(i, this.levels)
      if (j > i) {
        let temp: number = real[i]
        real[i] = real[j]
        real[j] = temp
        temp = imag[i]
        imag[i] = imag[j]
        imag[j] = temp
      }
    }

    // Cooley-Tukey decimation-in-time radix-2 FFT
    for (let size = 2; size <= this.n; size *= 2) {
      const halfsize: number = size / 2
      const tablestep: number = this.n / size
      for (let i = 0; i < this.n; i += size) {
        for (let j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
          const l: number = j + halfsize
          const tpre: number = real[l] * this.cosTable[k] + imag[l] * this.sinTable[k]
          const tpim: number = -real[l] * this.sinTable[k] + imag[l] * this.cosTable[k]
          real[l] = real[j] - tpre
          imag[l] = imag[j] - tpim
          real[j] += tpre
          imag[j] += tpim
        }
      }
    }

    this.calculateSpectrum(real, imag)

    // Returns the integer whose value is the reverse of the lowest 'bits' bits of the integer 'x'.
    function reverseBits (x: number, bits: number): number {
      let y = 0
      for (let i = 0; i < bits; i++) {
        y = (y << 1) | (x & 1)
        x >>>= 1
      }
      return y
    }
  }

  private calculateSpectrum (real: number[]|Float64Array, imag: number[]|Float64Array): void {
    // Should this be 4 / buffersize?
    const bSi = 4 / this.n
    let mag

    for (let i = 0, N = this.n / 4; i < N; i++) {
      mag = bSi * Math.sqrt(real[i] ** 2 + imag[i] ** 2)

      if (mag > this.peak) {
        this.peakBand = i
        this.peak = mag
      }

      this.spectrum[i] = mag
    }
  }
}

export default FFTNayuki