micarrsim/packages/acoustics-core/fractional-delay.js

import { fftInPlace } from "./fft.js";
import { interpolateFrequencyResponse } from "./frequency-response.js";
import { TAU } from "./math.js";

export function nextPowerOfTwo(value) {
  if (!Number.isFinite(value) || value < 1) throw new Error(`유효하지 않은 FFT 길이: ${value}`);
  let result = 1;
  while (result < value) result *= 2;
  return result;
}

export function prepareDelaySpectrum(samples, maximumDelaySamples = 0) {
  const fftSize = nextPowerOfTwo(samples.length + Math.ceil(maximumDelaySamples) + 2);
  const real = new Float64Array(fftSize);
  const imaginary = new Float64Array(fftSize);
  real.set(samples);
  fftInPlace(real, imaginary);
  return { real, imaginary, fftSize };
}

export function createDelayWorkspace(fftSize) {
  return { real: new Float64Array(fftSize), imaginary: new Float64Array(fftSize) };
}

export function addFrequencyDomainPaths(options) {
  const {
    output,
    spectrum,
    paths,
    gain = 1,
    phaseOffsetDeg = 0,
    frequencyResponse,
    sampleRate,
    workspace,
  } = options;
  if (!Array.isArray(paths) || paths.length === 0) {
    throw new Error("frequency-domain path가 하나 이상 필요합니다.");
  }
  for (const path of paths) {
    if (!(path.delaySamples >= 0) || !Number.isFinite(path.delaySamples)) {
      throw new Error("유효하지 않은 delay: " + path.delaySamples);
    }
    if (!Number.isFinite(path.gain)) throw new Error("path gain은 유한한 숫자여야 합니다.");
  }
  if (workspace.real.length !== spectrum.fftSize || workspace.imaginary.length !== spectrum.fftSize) {
    throw new Error("fractional-delay workspace 크기가 spectrum과 다릅니다.");
  }
  const hasFrequencyResponse = Array.isArray(frequencyResponse) && frequencyResponse.length > 0;
  if (hasFrequencyResponse && (!(sampleRate > 0) || !Number.isFinite(sampleRate))) {
    throw new Error("frequencyResponse 적용에는 유효한 sampleRate가 필요합니다.");
  }

  const size = spectrum.fftSize;
  const calibrationPhase = (phaseOffsetDeg * Math.PI) / 180;
  const response = {};
  workspace.real.fill(0);
  workspace.imaginary.fill(0);
  const halfSize = size / 2;
  const phaseReanchorInterval = 1024;
  for (const path of paths) {
    const phaseStep = (-TAU * path.delaySamples) / size;
    const stepReal = Math.cos(phaseStep);
    const stepImaginary = Math.sin(phaseStep);
    let phaseReal = 1;
    let phaseImaginary = 0;
    for (let bin = 0; bin <= halfSize; bin += 1) {
      workspace.real[bin] += phaseReal * path.gain;
      workspace.imaginary[bin] += phaseImaginary * path.gain;
      if (bin > 0 && bin < halfSize) {
        const negativeBin = size - bin;
        workspace.real[negativeBin] += phaseReal * path.gain;
        workspace.imaginary[negativeBin] -= phaseImaginary * path.gain;
      }
      const nextBin = bin + 1;
      if (nextBin % phaseReanchorInterval === 0) {
        phaseReal = Math.cos(phaseStep * nextBin);
        phaseImaginary = Math.sin(phaseStep * nextBin);
      } else {
        const nextReal = phaseReal * stepReal - phaseImaginary * stepImaginary;
        phaseImaginary = phaseReal * stepImaginary + phaseImaginary * stepReal;
        phaseReal = nextReal;
      }
    }
  }

  for (let bin = 0; bin < size; bin += 1) {
    const signedBin = bin <= size / 2 ? bin : bin - size;
    const phaseSign = signedBin === 0 ? 0 : signedBin > 0 ? 1 : -1;
    let responseGain = 1;
    let responsePhase = 0;
    if (hasFrequencyResponse) {
      interpolateFrequencyResponse(
        frequencyResponse,
        (Math.abs(signedBin) * sampleRate) / size,
        response,
      );
      responseGain = response.linearGain;
      responsePhase = response.phaseRadians;
    }
    const pathReal = workspace.real[bin];
    const pathImaginary = workspace.imaginary[bin];
    const responseAndCalibrationPhase = phaseSign * (calibrationPhase + responsePhase);
    const calibrationReal = Math.cos(responseAndCalibrationPhase) * responseGain * gain;
    const calibrationImaginary = Math.sin(responseAndCalibrationPhase) * responseGain * gain;
    const transferReal =
      pathReal * calibrationReal - pathImaginary * calibrationImaginary;
    const transferImaginary =
      pathReal * calibrationImaginary + pathImaginary * calibrationReal;
    const inputReal = spectrum.real[bin];
    const inputImaginary = spectrum.imaginary[bin];
    workspace.real[bin] =
      inputReal * transferReal - inputImaginary * transferImaginary;
    workspace.imaginary[bin] =
      inputReal * transferImaginary + inputImaginary * transferReal;
  }

  // A real sequence has a real-valued Nyquist coefficient. Projecting this single self-conjugate
  // bin back to the real axis preserves Hermitian symmetry for fractional delays.
  workspace.imaginary[size / 2] = 0;
  fftInPlace(workspace.real, workspace.imaginary, true);
  const outputLength = Math.min(output.length, workspace.real.length);
  for (let sampleIndex = 0; sampleIndex < outputLength; sampleIndex += 1) {
    output[sampleIndex] += workspace.real[sampleIndex];
  }
}

export function addFrequencyDomainDelay(options) {
  const { delaySamples, gain = 1, ...shared } = options;
  return addFrequencyDomainPaths({
    ...shared,
    paths: [{ delaySamples, gain }],
  });
}