FOF Vowel Synthesiser (C++)

A single-file C++17 command-line port of my Python FOF synthesis engine, implementing Rodet's time-domain Formant-Wave-Function (FOF) synthesis. No dependencies — just the standard library. Outputs 16-bit PCM WAV.

Build & run

g++ -std=c++17 -O2 -Wall -Wextra -o fof_synth fof_synth.cpp

./fof_synth --vowel a --f0 220 --dur 1.0 --sr 44100 --out vowel_a.wav
./fof_synth --vowel i --f0 220 --no-vibrato --out vowel_i_flat.wav
./fof_synth --help

Options: --vowel <a|i|u|o>, --f0 <Hz>, --dur <s>, --sr <Hz>, --out <file>, --no-vibrato, --test-tone.

What it does

Each formant is rendered as a repeating FOF grain — an exponentially decaying sinusoid at the formant centre frequency with a raised-cosine attack:

• attack (0 <= k <= pi/beta): 0.5 * (1 - cos(beta*k)) * exp(-alpha*k) * sin(omega_c*k)
• decay (k > pi/beta): exp(-alpha*k) * sin(omega_c*k)

where alpha = pi*BW/fs sets the -6 dB bandwidth and beta sets the attack time (~3 ms). Grains for all formants are overlap-added once per fundamental period. Grain length is truncated at the T60 decay time.

The fundamental is modulated by a CHANT-style f0 contour: sinusoidal vibrato (5.5 Hz, 12 cents) plus three-layer block-held random jitter, disabled with --no-vibrato.

Vowel formant data: Mandarin vowels (3 formants) from Chen & Wang (2011).

Validation against the Python version

Output was verified against the original Python implementation (same f0, sample rate, vibrato disabled):

Beyond the visual match, an averaged-spectrum comparison of the first 15 harmonics shows the two implementations agree to within 0.04 dB per harmonic (mean deviation 0.06 dB below 5 kHz) — i.e. numerically equivalent up to 16-bit quantisation.

Port notes (Python -> C++)

• NumPy vectorised grain synthesis becomes a per-sample loop with explicit bounds checking (operator[] does not clip like a Python slice).
• Buffers are std::vector<double> passed by reference and mixed with += (overlap-add).
• Random jitter uses std::mt19937 + std::normal_distribution; the noise sequence differs from NumPy's, so jitter is statistically equivalent but not bit-identical (validation is therefore done with vibrato disabled).
• dB formant amplitudes from the Python tables are pre-converted to linear.

References

1. X. Rodet, "Time-Domain Formant-Wave-Function Synthesis," Computer Music Journal, vol. 8, no. 3, 1984.
2. X. Rodet, Y. Potard, J.-B. Barriere, "The CHANT Project," Computer Music Journal, vol. 8, no. 3, 1984.
3. H. C. Chen and M. J. Wang, "An Acoustic Analysis of Chinese and English Vowels," 2011.