Also known as: unvoiced synthesis, noise-band synthesis, 6.4 synthesis
MBE unvoiced synthesis is the IMBE decoder stage — TIA-102.BABA §6.4 — that fills the noise-like portion of the speech spectrum, the bands the multi-band-excitation model marked unvoiced.1 Where the voiced synthesis generates deterministic sinusoids, §6.4 shapes filtered white noise: it takes a FFT of a noise block, keeps only the frequency bins that fall under unvoiced harmonics (scaled by those harmonics’ amplitudes), zeros the rest, transforms back, and stitches successive frames together with a windowed overlap-add so nothing clicks at the boundaries.
Shaping the noise spectrum
SynthUnvoicedFromNoise in internal/voice/mbe/synth_unvoiced.go runs the core pipeline:
interpret a length-256 noise buffer as a real time signal, forward-FFT it, shape the spectrum, and
inverse-FFT back. The shaping step, ShapeUnvoicedSpectrum, classifies every FFT bin by the
harmonic it falls under using IMBE’s nearest-centre rule, l = round(2π·k_eff / (N·ω₀)), and then:
- zeros the bin if the harmonic is voiced, or if it is outside the modelled range
[1..L]; - scales the bin by that harmonic’s linear amplitude
Ml[l]if the harmonic is unvoiced.
The mapping uses each bin’s effective frequency — bins above N/2 are mirrored back through the
conjugate symmetry — so both halves of a (k, N−k) pair get the same real scale factor. That keeps
the spectrum Hermitian-symmetric and guarantees the inverse transform is real-valued. The
FFT length is fixed at 256 (UnvoicedFFTSize): long
enough that each harmonic band spans several bins, short enough to stay cheap.
Windowed overlap-add
A 256-point frame is produced every 160 samples, so consecutive frames overlap by
UnvoicedTailSamples = 96 samples. The production path, SynthUnvoicedOverlapAdd, emits the
previous frame’s stored 96-sample tail into the start of the current frame, computes the new
windowed frame, adds its first 160 samples to the output, and stashes its last 96 for next time —
threading the overlap state through SynthState.PrevUnvoicedTail.
The synthesis window is chosen with care. Consecutive frames carry independent noise blocks, so
in the overlap region their variances add rather than their amplitudes. A plain periodic Hann
window at this 160-sample hop leaves the noise-power envelope rippling ~7 dB, which leaks through as
a 50 Hz frame-rate amplitude modulation — an audible buzzy tremolo on fricatives. §6.4’s window is
instead power-complementary at this hop: a flat unity top over the non-overlapping centre
[96, 160) with a quarter-wave sine taper of length 96 on each edge. Because a sine taper satisfies
w[n]² + w[95−n]² = 1, the summed noise power P[n] is flat to within 1e-9 across the whole frame,
so the tremolo vanishes while the taper still decays to zero at the edges to suppress boundary
clicks — and its flat top passes more aspiration energy than the Hann did.
Where it sits
Unvoiced synthesis is summed into the same output buffer as the voiced synthesis (both stages add
rather than overwrite), so a frame’s noise bands and harmonic bands combine into one waveform. Its
input amplitudes are the same enhanced, smoothed Ml the voiced path uses. Silent and zero-L
frames still emit the previous tail so a voiced→silent transition fades cleanly, then clear the
tail so the next frame starts fresh.
Relevance to SDR
The unvoiced band is what makes decoded speech sound like speech and not a buzzer: the breathy noise of fricatives (s, f, sh) and aspiration lives entirely here. Getting the overlap-add window right is a concrete example of a synthesis detail that is inaudible in a spectrum plot but obvious to the ear — it was one of the artifacts examined while chasing GopherTrunk’s “machine voice” report. Together with the voiced synthesis it completes the pure-Go P25 Phase 1 voice decoder.
Sources
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Multi-Band Excitation — Wikipedia, on the voiced/unvoiced band model whose unvoiced part §6.4 synthesizes. ↩