What AMBE actually is¶

AMBE is not a compression algorithm in the sense that ZIP or MP3 are compression algorithms. It does not try to store your voice more compactly. It throws your voice away, measures a handful of numbers about it fifty times a second, and sends those numbers. At the far end, a synthesizer that has never heard you builds a new voice from the numbers.

Understanding AMBE means understanding which numbers, why those, and how they are measured. This page covers the model — what the numbers mean. The next page covers how they are measured.

The problem: the bit budget is absurd¶

Telephone-bandwidth speech is sampled at 8 kHz with 16-bit samples, which is 128 000 bits per second. A D-STAR digital voice channel gives the vocoder 2400 bit/s, with a further 1200 bit/s of forward error correction on top, for 3600 bit/s of voice payload on the air JARL D-STAR system specification §1.1(3): "AMBE (2020) converting at 2.4 Kbps / FEC at 3.6 Kbps". The voice frames are 72 bits long and each one represents 20 ms of speech JARL D-STAR spec §2.1.2(2).

That is a factor of 53 below the PCM rate. There is no waveform coder that survives that. At 2400 bit/s you have roughly 48 bits per 20 ms of speech — about six bytes to describe a syllable's worth of a human being. You cannot describe a waveform in six bytes. You can only describe a model of the thing that produced it, and hope the model is good enough that a reconstruction from its parameters is still recognisably a person saying a word.

So every low-rate speech coder is a bet on a model. The interesting question is which bet.

Before any of the argument, here is the answer in one clip: what a coder actually takes away from a fifth of a second of somebody talking.

Two ways to model a voice¶

The classical bet is the source–filter model. Speech is treated as the response of a system to an excitation: you estimate the excitation parameters and the system parameters separately, then, to synthesize, generate an excitation signal — "a periodic impulse train in voiced regions or random noise in unvoiced regions" — and filter it with the estimated system Griffin & Lim 1988, §I. This is the LPC vocoder family, and its defining feature is a single voiced/unvoiced decision per frame. Each 20 ms of speech is declared either buzz or hiss, wholesale.

The competing bet is the sinusoidal model: describe the short-time spectrum as a sum of sine waves at the harmonics of a fundamental, and code their amplitudes (and, in some systems, their phases). This handles voiced speech beautifully and noise badly — noise has no harmonics to code, so harmonic coders end up spending four or five bits per harmonic on phase just to make noisy regions sound like noise Griffin & Lim 1988, §II.

Both bets fail in the same place, and the failure has a name: buzziness. Griffin and Lim state the diagnosis precisely. Speech synthesized entirely from a periodic source sounds buzzy; speech synthesized entirely from a noise source sounds hoarse; and real speech regions — mixed voicing, or voiced speech recorded in noise — have parts of the spectrum dominated by harmonics and other parts, at the same instant, dominated by noise-like energy. A single voiced/unvoiced switch has to pick one, so it replaces the noise-like energy with periodic energy, and that substitution is what the ear hears as buzz Griffin & Lim 1988, §I.

It gets worse in noise. Gold and Tierney's measurements, quoted in the paper, showed a contemporary 2400 bit/s vocoder costing 18.7 DRT intelligibility points against uncoded speech in F15 noise, but only 10.3 points against uncoded speech in the clean condition. Both figures are vocoder-versus-uncoded gaps; the extra 8.4 points that the noise condition costs is what they named the vocoder's "aggravation factor" Griffin & Lim 1988, §I, citing Gold & Tierney. The paper's hypothesis for where those points go is worth sitting with: listeners use the distinction between "this frequency region is periodic" and "this frequency region is noise" to pull a voice out of a noisy background, and a single-decision vocoder destroys that cue before the listener ever gets it Griffin & Lim 1988, §I.

The multi-band idea¶

Here is the whole trick.

Take the windowed speech segment s_w(n) = w(n) · s(n) Griffin & Lim 1988, eq. 1 and model its Fourier transform as a product of two things — a spectral envelope and an excitation spectrum magnitude:

S_w(ω) = H_w(ω) · |E_w(ω)|

Griffin & Lim 1988, eq. 2

So far this is just source–filter written in the frequency domain. The envelope H_w(ω) is a smoothed version of the speech spectrum, the same role LPC coefficients or cepstral coefficients play Griffin & Lim 1988, §II.

The departure is in |E_w(ω)|. In the simple models, the excitation spectrum is fully specified by the fundamental frequency ω₀ plus one voiced/unvoiced bit for the entire spectrum. In the MBE model it is specified by ω₀ plus a frequency-dependent voiced/unvoiced function. A continuously varying mixture function would cost too many parameters to transmit, so it is restricted to a binary decision, and then the spectrum is divided into bands with one binary decision per band Griffin & Lim 1988, §II.

The number of bands is the point. Earlier mixed-excitation vocoders had used "three frequency bands at most"; the MBE model divides the spectrum into "a large number of frequency bands (typically 20 or more)", potentially one per harmonic of the fundamental Griffin & Lim 1988, §II. That is where the name comes from, and it is the entire difference between MBE and everything that came before it.

Before going on, spend a moment with the comb. Drag the fundamental from a deep voice to a high one and watch how many teeth stay inside the coded band: that count is the number of amplitudes the coder has to pay for, and it changes by a factor of five across ordinary human voices.

The excitation spectrum is then assembled band by band: segments of a periodic spectrum |P_w(ω)| in the bands declared voiced, segments of a random noise spectrum |U_w(ω)| in the bands declared unvoiced Griffin & Lim 1988, §II. The periodic spectrum is completely determined by ω₀ alone — you can get it as the Fourier transform magnitude of a windowed impulse train at the pitch period, or equivalently by centering the transform of the analysis window on every harmonic of ω₀ and summing Griffin & Lim 1988, §II. It costs no bits beyond the pitch.

PSEUDOCODE — the model, stated as a recipe (NOT EXECUTABLE)

given  ω₀            the fundamental frequency for this frame
       v[1..K]       one binary voiced/unvoiced flag per frequency band
       A[1..L]       one envelope sample per harmonic of ω₀

for each frequency ω in the analysis band:
    let b ← the band index containing ω
    if v[b] says voiced:
        excitation(ω) ← periodic spectrum at ω, which follows from ω₀ alone
    else:
        excitation(ω) ← noise spectrum at ω, normalised to unit average
                        magnitude across the band
    envelope(ω)  ← interpolate between the harmonic samples A[·]
                   that straddle ω
    spectrum(ω)  ← envelope(ω) × excitation(ω)

The consequence: one bit buys you the ability to say "this 500 Hz slice of this 20 ms of speech is breath, and the slice below it, simultaneously, is voice." A vowel with a breathy top end, a voiced fricative, a word spoken over engine noise — all of these are representable rather than approximated.

The figure below is that claim, measured. Play a clip and watch the eight bands change colour independently: find a frame where the bottom bands are periodic and the top ones are not, and you are looking at the case a single-decision vocoder cannot represent.

The parameters, and what they cost¶

The envelope is represented by one sample per harmonic of the fundamental — in voiced and unvoiced regions alike — because that is the cheapest representation that stays tied to the excitation structure. When the synthesizer needs a densely sampled envelope, it linearly interpolates between the harmonic samples Griffin & Lim 1988, §II.

So the per-frame parameter set is:

US 5,754,974 (Griffin & Hardwick, DVSI, filed 1995, issued 1998), Background: "a fundamental frequency ... a set of V/UV decisions which characterize the voicing state; and a set of spectral amplitudes which characterize the spectral envelope"

The number of harmonics is not free — it falls out of the pitch, since harmonics of a low fundamental are packed more densely into the same bandwidth. The patents give it as L = ⌊α·π/ω₀⌋, where α sets the coded bandwidth as a fraction of Nyquist; the 3.6 kbit/s system at 8 kHz sampling uses α = 0.925, giving a coded bandwidth of 3700 Hz US 5,754,974; US 5,701,390. A low-pitched voice therefore has more parameters to transmit in the same 72 bits than a high-pitched one, which is a tension that runs through the whole quantizer design.

One parameter is conspicuously missing from that table: phase. The original 1988 coder did transmit the phase of each voiced harmonic, and spent a large share of its 160 bits per frame doing so Griffin & Lim 1988, §II and §V-A. Every production descendant dropped it, and the decoder regenerates phase instead. That is a synthesis-side story, told on the synthesis page.

Did it work?¶

Yes, and the paper measured it against the fairest possible control: the same coder with the multi-band decision removed. The Single Band Excitation coder used "exactly the same parameters as the Multiband Excitation Speech Coder, except that one V/UV bit per frame is used instead of 12" Griffin & Lim 1988, §V.

Diagnostic Rhyme Test scores, where 100 is perfect and guessing scores zero:

Griffin & Lim 1988, Abstract and Tables III–IV

On clean speech the two are indistinguishable — 96.2 against 96.0. In noise the multi-band model is twelve points better, landing about five points below the uncoded noisy speech instead of seventeen. The paper's spectrogram analysis of the /h/ in "has" shows why: several harmonics of the fundamental in the low-frequency region with the upper region dominated by aperiodic energy, reproduced faithfully with 12 V/UV bits, and flattened into harmonics-everywhere by the single-decision coder Griffin & Lim 1988, §V-B, Figs. 12–13.

Twelve bits. That is the entire cost of the idea.

Where AMBE sits in the family¶

The lineage is one model, re-quantized downward three times, with the analysis and synthesis machinery hardened at each step.

MBE (1988) — the research coder in the paper. 10 kHz sampling, 25.6 ms Hamming analysis window, 50 Hz frame rate, 160 bits per frame for an 8 kbit/s total, 12 V/UV bands, and coded harmonic phases Griffin & Lim 1988, §V-A.

IMBE — "Improved Multiband Excitation", 7.2 kbit/s at a 50 Hz frame rate, 144 bits per frame. Of those, 57 bits go to forward error correction and synchronisation and 87 to the model parameters, split as 8 bits for the fundamental frequency, K bits for the voiced/unvoiced decisions, and 79 − K bits for the spectral amplitudes; the patent also describes a 6.4 kbit/s variant for satellite use US 5,630,011 (Lim & Hardwick, DVSI, filed 1994, issued 1997). This is the generation used by APCO Project 25.

AMBE — the 3.6 kbit/s system, and the one this site is about. 72 bits per 20 ms frame, allocated as 7 bits for the fundamental frequency, 8 bits for the V/UV decisions over eight bands of approximately 500 Hz spanning 0–4 kHz, and the remaining 57 bits for the spectral magnitudes US 5,754,974, describing the 3.6 kbps system. Take the 7 + 8 + 57 split as the patent's worked example rather than as D-STAR's frame, because it is a system in which all 72 bits carry parameters. D-STAR uses a lower-rate member of the same family: 2400 bit/s of speech data — 48 bits per 20 ms frame — plus 1200 bit/s of FEC, packed into the same 72-bit, 20 ms frame on the air JARL D-STAR spec §1.1(3), §2.1.2(2). How those 48 parameter bits are divided is not published anywhere; quantization explains the structure they must have, and what is not in the public record records the gap.

AMBE+2 — the later half-rate generation, used by DMR, YSF and NXDN. It is a real system and it exists. US 8,359,197, "Half-rate vocoder" (Hardwick, DVSI, issued 2013), is listed as active with an anticipated expiry of 20 May 2028; see the patents page. This site sticks to full-rate AMBE and IMBE, the codec D-STAR uses, because that is its subject.

What the model does not contain¶

There is no vocal tract in this model. No lips, no glottis, no formant tracker, no articulatory anything. There is a fundamental frequency, a set of yes/no answers to "is this band buzz or hiss", and a set of amplitudes. The model is deliberately ignorant of why the spectrum looks the way it does; it only cares that a synthesizer given these numbers produces a spectrum close to the original one.

Which raises the question the whole design turns on: close by what measure, and how do you find the parameters that get you there? That is analysis.

Next: Analysis: pitch, voicing, amplitudes. How 20 ms of microphone audio becomes one pitch, eight flags and a list of amplitudes, and why the estimating is harder than the modelling. Back to the start. If you would rather hear the thing before reading about it, Listen has eight sentences before and after a real codec chip.

Last reviewed: 2026-08-10.