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Acoustic localization · Planned build files · Rev. Oct 22, 2026

Four microphones, one clock, and the direction a clap came from.

A 150 mm square of four digital MEMS microphones on a Teensy 4.1. When it hears a sharp sound, such as a clap, a wooden clapper or a balloon pop, it measures the arrival-time differences across the array and reports the bearing. Bench and indoor tests only.

Companion: Hammerhead speed quad build files ↗.

Microphones4 INMP441, digital I2S

Array150 mm square

Max delay437 µs, adjacent pair

Parts cost$65.95 bought, Oct 2026

A / Bill of materials

The whole array for under $70

Prices are what I paid on Oct 11, 2026, in USD before tax and shipping. The frame is printed, and the clock and data wiring fits on one perfboard.

Qty	Part	Why	Source	Each	Line

Why a Teensy and not an ESP32 or Arduino: its audio library reads two I2S data lines on one shared clock, so all four channels are sampled at exactly the same instants. Direction finding lives on those instants.

B / Wiring & geometry

Two data lines, one shared clock

INMP441 mics share data lines in pairs: each mic is strapped left or right and only talks in its half of the frame. Four mics need two data lines, and all of them run from the same bit clock and word clock.

Top view, to scale. Bearing is measured clockwise from the front edge, between M1 and M2.Fig. B1

Wiring matrix

Pin by mic

Teensy 4.1	M1	M2	M3	M4
3.3 V	VDD	VDD	VDD	VDD
GND	GND	GND	GND	GND
`21` · BCLK1	SCK	SCK	SCK	SCK
`20` · LRCLK1	WS	WS	WS	WS
`8` · RX data 1	SD	SD	—	—
`6` · RX data 2	—	—	SD	SD
L/R strap	GND · left	3.3 V · right	GND · left	3.3 V · right
Audio channel	1	2	3	4

Before you solder

Data-line pins 8 and 6 are the Teensy 4 audio library's quad-input pins as I understand them. Check them against PJRC's current pin map first, then confirm the channel order with the tap test (A01). Wire lengths don't need matching: 10 cm of wire delays the signal by under a nanosecond, against a 22.7 µs sample.

Connection schedule

7 runs

#	Run	Wire	Notes

C / Method

From a clap to a bearing

The firmware waits for an onset, grabs the same window from all four channels, finds the delay between every pair with GCC-PHAT, and solves for the direction that best explains all six delays at once.

Signal chain

Teensy firmware

01CaptureFour mics, one I2S clock, 44.1 kHz, 16 bits kept.

02Buffer200 ms ring buffer per channel so the onset is never cut off.

03DetectShort-term energy 15 dB above the running noise floor.

04Window4,096 samples (93 ms) around the onset.

05GCC-PHATSix pairs. Peak searched only inside the physical delay limit, then a sub-sample fit.

06SolveLeast squares for the arrival direction; bearing from atan2.

07LogBearing over USB serial; the 4-channel clip to microSD.

The math

Far-field, 2D

t_i = −(p_i · u) / c

Arrival time at mic i, at position p_i, for a plane wave travelling from direction u at sound speed c.

τ_ij = t_i − t_j = (p_j − p_i) · u / c

Six pairs give six equations in the two unknown components of u. Least squares, normalize, then bearing θ = atan2(u_x, u_y).

R_ij(τ) = IFFT[ X_i X_j^* / |X_i X_j^*| ], τ_ij = argmax R_ij

GCC-PHAT keeps only phase, which sharpens the correlation peak and resists room echoes better than plain cross-correlation.

Resolution and error sources

150 mm array

Quantity	Value	Basis
Speed of sound, 20 °C	343.4 m/s	331.3 + 0.606·T
One sample at 44.1 kHz	22.7 µs	7.8 mm of travel
Bearing per whole sample, broadside	3.0°	c·Δt / d
With sub-sample peak fit	0.3–0.6°	estimate
Near-field bias, source at 1 m	0.08°	Exact geometry vs. plane wave
Near-field bias, source at 0.5 m	0.32°	Same
Bias from a 10 °C error in c	about 1° at 45°	c sets the delay-to-angle scale
Processing per event	a few ms	estimate 10 FFTs of 4,096 points

Elevation shrinks all six delays by the same factor, cos(elevation). The normalized bearing survives, and the shrink factor is a rough elevation estimate (without telling up from down).

Procedure

Three weeks

Channel map. Tap each mic with a pencil; confirm which channel spikes.
Sync check. Tap the exact centre of the frame. All six delays should be zero.
End-on delays. Clap in line with a side pair, then a diagonal pair, at 2 m.
Bearing sweep. Quiet room, array on a table over a printed protractor ring, source at array height. 12 bearings at 2 m and 4 m, 10 claps each.
Hallway. Repeat the sweep somewhere with strong echoes.
Detection. 50 claps at 3 m, then 30 minutes of ordinary room noise with no claps.

Sound sources

Safe and repeatable

Source	Use	Note
Hand clap	Most tests	Varies clap to clap; fine for averages.
Wooden clapper	Bearing sweep	Two boards on a hinge; the most repeatable onset.
Balloon pop	Occasional	Keep at least 2 m away; close up it can exceed the mic's 120 dB SPL limit.
Pencil tap on a mic	Channel map	Hits one channel only.

D / Test log

Each prediction, and how it gets tested

Predictions and pass bands are written before testing, so a result can't be explained away later. A miss gets reported here like any other result.

Planned build document — not measured test results. Every test entry is a prediction or proposed pass band; no measured results are reported here.

ID	Quantity	Predicted	How it's measured	Pass band	When	Measured	Status

Limits of this study

One array, indoors, with claps. Results describe this geometry in these rooms. Outdoor wind, distant sources and echoes off buildings are a different problem, and the spread-out field version is where that gets tested.