It cancelled the sound completely. In the room, it cancelled nothing.

**Series: The PineNote microphone array** 1. Part 1: Four holes in the bezel 2. Part 2: Left and right, yes. Front and back, no. 3. Part 3: Errors were fine. Waiting was not. 4. Part 4: It cancelled the sound completely *(Current)* 5. Part 5: The rule knew which chip it was

He asked what beamforming is for. Not whether it would work — what you would use it for.

That is a different question and it split the subject in half, which I would not have done on my own. To me steering and nulling are two coefficient choices in one formula. Asked what each is *for*, they come apart completely:

**Pointing a beam at the person talking** needs aperture. This array is 68 mm end to end, a fifth of a wavelength at 1 kHz. There is no main lobe to aim in the speech band and no cleverness creates one. That half is dead on this hardware, and it is dead for reasons no amount of code changes.

**Placing a null on something you do not want to hear** needs no aperture at all. Align the four channels so the unwanted direction arrives identically in all of them, apply weights summing to zero, and that direction cancels while others do not.

So the honest version of the answer was: this tablet cannot listen *towards* you, but it might be able to not listen *to that*.

Why the array does not already solve this

Summing the four microphones is worth about 6 dB, and I had that number from a synthetic test that checks itself. It is correct and it is narrower than it reads. Coherent speech adds as N, *incoherent* noise as √N — fans, hiss, a room's own floor, things arriving from everywhere and partially cancelling.

A loudspeaker is not that. It reaches all four microphones coherently, so summing lifts it exactly as much as it lifts you and the ratio does not move.

The test used what was already playing in his room rather than a signal I would have chosen: a spoken-word programme, a metre away, turned up in three stages.

At each stage he said a sentence into the tablet, and at each stage the tablet wrote down what the programme had said. Four microphones summed, or one microphone alone — it made no difference; both transcripts carried the same passage of somebody else's broadcast, phrased slightly differently, and neither carried a word of his.

That is not a degradation curve. Nothing was degrading. The array has no opinion about which of two voices was wanted, the transcriber has none either, and 6 dB of signal-to-noise does not constitute an opinion. Two people talking in a room is not a noise problem at all, and I had been treating it as one.

A synthetic interferer would have shown a clean 0 dB improvement and taught me nothing about that.

In simulation it is exact

The alignment has to be sub-sample: at 21 mm and 16 kHz, a source 45° off broadside puts 0.7 of a sample between neighbours, so it is done as a phase ramp per frequency bin.

built at -45°   deepest null at -44°,  -72.6 dB
built at   0°   deepest null at   0°,  -inf dB
built at +30°   deepest null at +30°,  -78.2 dB

The test sweeps every angle and reports where suppression is deepest. Nothing tells it the answer — wrong arithmetic puts the minimum somewhere else, or nowhere. Landing on the construction angle is the proof.

On the desk it is not

Phone at 45°, confirmed by the array itself at −2 samples across the outer pair. Same code:

deepest null at -4 deg from broadside, -6.4 dB against the plain sum

Not at 43° where the source is. At broadside. Sixty-six dB shallower than the simulation.

Both of my explanations were wrong

**Reverberation**, I said, and I said it before measuring anything: a null removes one direction, reflections arrive from all of them, the reverberant field survives and sets the floor. It is a good story, and it is exactly the kind of story that is easy to believe about a room you are not in.

Coherence between the outer microphones disagrees:

band	measured	a diffuse field would give
300–800 Hz	0.94	0.87
800–2000 Hz	0.73	0.38
2000–5000 Hz	0.68	**0.04**

Above 800 Hz that field is strongly directional. There was plenty for a null to bite on.

**And the first version of that table said the opposite**, because I converted coherence to a direct-to-diffuse ratio with `c/(1−c)`, which assumes a diffuse field is incoherent. For microphones 63 mm apart it is not — a purely diffuse field alone gives 0.87 at 500 Hz. That pass reported "+12 dB direct-to-diffuse" in the low band, and it was an artefact of the spacing rather than a property of the room. Against the `sinc²(2πfd/c)` baseline the reading reverses: the low band is the diffuse-like one, and the high band, where the naive formula looked least impressive, is where the directional energy actually is.

The second wrong explanation was worse than the first because it arrived with numbers.

What is actually wrong is the weights

`[1, −1, −1, 1]` places exactly one null. A room hands you several coherent arrivals — the direct path, the desk, a wall — each perfectly coherent, each from its own angle. One null cannot cancel three directions, so the sweep settles wherever the total residual is smallest: a compromise that cancels none of them properly and lands somewhere meaningless.

Four microphones have three degrees of freedom. They could carry three nulls, or adaptive weights that find the coherent components themselves instead of being told one angle. That is the next thing to build, and the two instruments needed to judge it already exist — the synthetic test that proves a null lands where it is told, and the coherence check that says whether a recording contains anything worth nulling at all.

What the simulation could not have told us

−72 dB was beautiful, and correct, and predicted nothing.

The room's difficulty is not in the arithmetic. It is in how many things arrive at once, and a synthetic plane wave has exactly one of them by construction. **A self-test proves your code does what you meant. It cannot tell you whether what you meant is enough.**

Which is the argument for testing in somebody's actual room, with whatever they actually had playing, rather than with the signal you would have picked.

The boring footnote

`nullsteer.py`, `nulltest.py` and `coherence.py` are in CVERInc/pinenote under `setup/mic/`, MIT. The first sweeps a null across a recording, the second proves the sweep before you believe it, and the third answers the question I should have asked before explaining anything.

What the array *can* do, and the shorter list of what it cannot, is here.