Pea whistle steganography

Would anyone notice if a referee's whistle transmitted a secret data burst?

I do really follow the game. But every time the pea whistle sounds to start the jam I can't help but think of the possibility of embedding data in the frequency fluctuation. I'm sure it's alternating between two distinct frequencies. Is it really that binary? How random is the fluctuation? Could it be synthesized to contain data, and could that be read back?

I found a staggeringly detailed Wikipedia article about the physics of whistles – but not a single word there about the effects of adding a pea inside, which is obviously the cause of the frequency modulation.

To investigate this I bought a metallic pea whistle, the Acme Thunderer 60.5, pictured here. Recording its sound wasn't straightforward as the laptop microphone couldn't record the sound without clipping. The sound is incredibly loud indeed – I borrowed a sound pressure meter and it showed a peak level of 106.3 dB(A) at a distance of 70 cm, which translates to 103 dB at the standard 1 m distance. (For some reason I suddenly didn't want to make another measurement to get the distance right.)

Later I found a microphone that was happy about the decibels and got this spectrogram of a 500-millisecond whistle.

The whistle seems to contain a sliding beginning phase, a long steady phase with frequency shifts, and a short sliding end phase. The "tail" after the end slide is just a room reverb and I'm not going to need it just yet. A slight amplitude modulation can be seen in the oscillogram. There's also noise on somewhat narrow bands around the harmonics.

The FM content is most clearly visible in the second and third harmonics. And seems like it could very well fit FSK data!

Making it sound right

I'm no expert on synthesizers, so I decided to write everything from scratch (whistle-encode.pl). But I know the start phase of a sound, called the attack, is pretty important in identification. It's simple to write the rest of the fundamental tone as a simple FSK modulator; at every sample point, a data-dependent increment is added to a phase accumulator, and the signal is the cosine of the accumulator. I used a low-pass IIR filter before frequency modulation to make the transitions smoother and more "natural".

Adding the harmonics is just a matter of measuring their relative powers from the spectrogram, multiplying the fundamental phase angle by the index of the harmonic, and then multiplying the cosine of that phase angle by the relative power of that harmonic. SoX takes care of the WAV headers.

Getting the noise to sound right was trickier. I ended up generating white noise (a simple rand()), lowpass filtering it, and then mixing a copy of it around every harmonic frequency. I gave the noise harmonics a different set of relative powers than for the cosine harmonics. It still sounds a bit too much like digital quantization noise.

Embedding data

There's a limit to the amount of bits that can be sent before the result starts to sound unnatural; nobody has lungs that big. A data rate of 100 bps sounded similar to the Acme Thunderer, which is pretty much nevertheless. I preceded the burst with two bytes for bit and byte sync (0xAA 0xA7), and one byte for the packet size.

Here's "OHAI!":

Sounds legit to me! Here's a slightly longer one, encoding "Help me, I'm stuck inside a pea whistle":

Homework

1. Write a receiver for the data. It should be as simple as receiving FSK. The frequency can be determined using atan2, a zero-crossing detector, or FFT, for instance. The synchronization bytes are meant to help decode such a short burst; the alternating 0s and 1s of 0xAA probably give us enough transitions to get a bit lock, and the 0xA7 serves as a recognizable pattern to lock the byte boundaries on.
2. Build a physical whistle that does this!

The microphone bioamplifier

As the in-ear microphone in the previous post couldn't detect a signal that would suggest objective tinnitus, the next step would be to examine EMG signals from facial muscles. This is usually done using a special-purpose device called a bioamplifier, special-purpose electrodes, and contact gel, none of which I have at hand. A perfect opportunity for home-baking, that is!

There's an Instructable called How to make ECG pads & conductive gel. Great! Aloe vera gel and table salt for the conductive gel are no problem, neither are the snap buttons for the electrodes. I don't have bottle caps, though, so instead I cut circular pieces out of some random plastic packaging.

As for the bioamplifier, why can't we just use the microphone preamplifier that was used for amplifying audio in the previous post? Both are weak low-frequency signals. There's no apparent reason for why it couldn't amplify EMG, if only a digital filter was used to suppress the mains hum.

It's a signal, but it's noise

First, a little disclaimer. It's unwise to just plug yourself into a random electric circuit, even if Oona survived. Mic preamps, for example, are not mere passive listeners; instead they will in some cases try to apply phantom power to the load. This can be up to 48 volts DC at 10 mA. There's anecdotal evidence of people getting palpitations from experiments like this. Or maybe not. But you wouldn't want to take the risk.

So I attached myself into some leads, soldered into a stereo miniplug, using the home-made pads that I taped on opposite sides of my face. I plugged the whole assembly into the USB sound card's mic preamp and recorded the signal at a pretty low sampling rate.

The signal, shown here from 0 to 700 Hz, is dominated by a mains hum (colored red-brown), as I suspected. There is indeed a strong signal present during contraction of jaw muscles (large green area). Moving the jaw left and right produces a very low-frequency signal instead (bright green splatter at the bottom).

It's fun to watch but still a bit of a disappointment; I was really hoping for a clear narrow-band signal near the 65 Hz frequency of interest.

Einthoven's triangle

At this point I was almost ready to ditch the EMG thing as uninteresting, but decided to move the electrodes around and see what kind of signals I could get. When one of them was moved far enough, a pulsating low-frequency signal would appear:

Could this be what I think it is? To be sure about it I changed the positions of the electrodes to match Lead II in Einthoven's triangle, as used in electrocardiography. The signal from Lead II represents potential difference between my left leg and right arm, caused by the heart.

After I plugged the leads in the amp already did this:

Looks promising! The mains hum was really irritating at this point, but I could get completely rid of it by rejecting all frequencies above 45 Hz, since the signal of interest was below that.

The result is a beautiful view of the iconic QRS complex, caused by ventricular depolarization in the heart:

Quite a side product!