fourier-transform

fourier-transform

FFT for real and complex signals. Split-radix real FFT + radix-2 complex FFT. Precomputed twiddle factors, typed-array buffers, zero dependencies.

Usage

import rfft from 'fourier-transform'

// magnitude spectrum (N/2 bins)
const spectrum = rfft(waveform)

import { fft } from 'fourier-transform'

// complex DFT of real input (N/2+1 bins, unnormalized)
const [re, im] = fft(waveform)

import { cfft, cifft } from 'fourier-transform'

// in-place complex FFT / inverse FFT
const re = new Float64Array(N), im = new Float64Array(N)
cfft(re, im)   // forward
cifft(re, im)  // inverse (1/N normalized)

API

rfft(input, output?) — default export

Returns magnitude spectrum as Float64Array of length N/2.

• input — Float32Array, Float64Array, or plain Array. Length must be power of 2 (>= 2).
• output — optional Float64Array(N/2) to write into.
• Returns internal buffer if no output provided (overwritten on next call with same N).

Normalization: a unit-amplitude cosine at frequency bin k produces spectrum[k] = 1.0.

fft(input, output?) — named export

Returns complex DFT as [re, im], each Float64Array of length N/2+1 (DC through Nyquist).

• output — optional [Float64Array(N/2+1), Float64Array(N/2+1)].
• Unnormalized: X[k] = sum( x[n] * e^(-j*2*pi*k*n/N) ).
• DC and Nyquist bins always have im = 0 (real input).

ifft(re, im, output?) — named export

Inverse of fft() — recovers time-domain signal from complex spectrum. Returns Float64Array of length N.

• re, im — Float64Array of length N/2+1 (as returned by fft()).
• im[0] and im[N/2] are ignored (half-complex format has no slot for them).
• Native split-radix DIF inverse — no complex FFT overhead.

const [re, im] = fft(signal)
// modify spectrum...
const recovered = ifft(re, im)

cfft(re, im) — named export

In-place complex forward FFT (unnormalized). Both re and im must be Float64Array of equal power-of-2 length (>= 2). Modifies arrays in place.

cifft(re, im) — named export

In-place complex inverse FFT (1/N normalized). Same signature as cfft.

STFT

import { stft, istft, stftBatch, stftStream, stftAnalysisStream } from 'fourier-transform/stft'

stft(signal, opts?) — analysis

Returns an array of frames, each with { re, im, mag, phase, time }.

• signal — Float32Array, Float64Array, or plain Array.
• opts.frameSize — FFT size, power of 2. Default: 2048.
• opts.hopSize — hop between frames. Default: frameSize / 4.
• time is the sample index of the frame centre in the original signal.
• Zero-padded by frameSize at front and back so edge samples are fully windowed.

const frames = stft(waveform, { frameSize: 2048, hopSize: 512 })
for (const f of frames) {
  console.log(f.time, f.mag[100]) // time in samples, magnitude at bin 100
}

istft(frames, opts?) — synthesis

Reconstructs a time-domain signal from STFT frames.

• frames — array of { mag, phase, time? } or { re, im, time? } objects.
• opts.signalLength — expected output length. Inferred from last frame if omitted.
  • When inferred, the tail may include padding; pass signalLength for exact control.
• Returns Float64Array.
• If re/im are present, they are used directly (no polar round-trip). Otherwise mag/phase are converted to cartesian.

const recovered = istft(frames, { frameSize: 2048, hopSize: 512, signalLength: waveform.length })

stftBatch(data, process, opts?) — batch with callback

Processes each frame through a callback and overlap-adds the result.

• process(mag, phase, state, ctx) → { mag, phase }
  • mag, phase — Float64Array(half + 1)
  • state — persistent object across frames
  • ctx — { N, half, hop, anaHop, synHop, freqPerBin, frameStart, sampleRate, opts }
    • ctx.frameStart — sample index of the frame start in the original signal. Negative at boundaries due to zero-padding.
    • ctx.opts — cloned copy of opts. Use this to pass custom parameters (e.g. ratio, ratioFn) through to your process callback.
• opts.anaHop — analysis hop (default: hopSize).
• opts.synHop — synthesis hop (default: hopSize). When anaHop !== synHop, the output is time-stretched or compressed.
• Returns Float32Array of length round(data.length * synHop / anaHop) (same as input when anaHop === synHop).

const result = stftBatch(signal, (mag, phase, state, ctx) => {
  // Simple spectral gate
  for (let k = 0; k < mag.length; k++) if (mag[k] < 0.1) mag[k] = 0
  return { mag, phase }
}, { frameSize: 2048, hopSize: 512 })

stftStream(process, opts?) — streaming with callback

Streaming version of stftBatch. Returns { write(chunk), flush() }.

• Supports opts.anaHop / opts.synHop for time-stretching in streaming context.

const stream = stftStream((mag, phase) => ({ mag, phase }), { frameSize: 2048 })

for (const chunk of audioChunks) {
  const processed = stream.write(chunk)
  // emit processed...
}
const tail = stream.flush()

stftAnalysisStream(opts?) — streaming analysis

Streaming version of stft. Returns { write(chunk), flush() } that emit frames.

• Supports opts.anaHop for non-uniform analysis spacing.

const stream = stftAnalysisStream({ frameSize: 2048, hopSize: 512 })
const frames = stream.write(chunk1)
frames.push(...stream.write(chunk2))
frames.push(...stream.flush())

View semantics

rfft, fft, and ifft return internal cached buffers by default. The next call with the same N overwrites the previous result. Pass an output buffer to keep results across calls:

const out = new Float64Array(N / 2)
rfft(signal, out) // safe to keep

Performance

N=4096 real-valued FFT, complex output, 20k iterations (lower is better):

fft.js (indutny)          16.5µs  ×1.0  — radix-4, interleaved output
fourier-transform         17.8µs  ×1.1  — split-radix, separate re/im
ooura                     23.6µs  ×1.4  — Ooura C port
ml-fft                    37.0µs  ×2.2
dsp.js                    48.1µs  ×2.9  — our split-radix ancestor
kissfft-wasm              49.4µs  ×3.0  — WASM KissFFT
ndarray-fft               63.1µs  ×3.8
als-fft                 2311.4µs  ×140
fft-js                  2329.2µs  ×141  — naive recursive

Raw transform speed is identical to fft.js. The gap is the cost of returning separate re/im arrays vs interleaved output.

npm run benchmark to reproduce.

Acknowledgments

Forward split-radix real FFT from dsp.js by @corbanbrook, derived from RealFFT. Inverse split-radix DIF algorithm from FXT by Joerg Arndt.

License

MIT

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