The Fourier transform

The Unreasonable Effectiveness Of The Fourier Transform

A talk, The Unreasonable Effectiveness of the Fourier Transform, was presented by [Joshua Wise] at Teardown 2025 in June last year. Click-through for the notes or check out the video below the break for the one hour talk itself.

The talk is about Orthogonal Frequency Division Multiplexing (OFDM) which is the backbone for radio telecommunications these days. [Joshua] tries to take an intuitive view (rather than a mathematical view) of working in the frequency domain, and trying to figure out how to “get” what OFDM is (and why it’s so important). [Joshua] sent his talk in to us in the hope that it would be useful for all skill levels, both folks who are new to radio and signal processing, and folks who are well experienced in working in the frequency domain.

If you think you’ve seen “The Unreasonable Effectiveness of $TOPIC” before, that’s because hacker’s can’t help but riff on the original The Unreasonable Effectiveness of Mathematics in the Natural Sciences, wherein a scientist wonders why it is that mathematical methods work at all. They seem to, but how? Or why? Will they always continue to work? It’s a mystery.

Hidden away in the notes and at the end of his presentation, [Joshua] notes that every year he watches The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever? and every year he understands a little more.

If you’re interested in OFDM be sure to check out AI Listens To Radio.

Continue reading “The Unreasonable Effectiveness Of The Fourier Transform”

When [Elon] Says No, Just Reverse Engineer The Starlink Signal

We all know that it’s sometimes better to beg forgiveness than ask permission to do something, and we’ll venture a guess that more than a few of us have taken that advice to heart on occasion. But [Todd Humphreys] got the order of operations a bit mixed up with his attempt to leverage the Starlink network as a backup to the Global Positioning System, and ended up doing some interesting reverse engineering work as a result.

The story goes that [Todd] and his team at the University of Texas Austin’s Radionavigation Lab, on behalf of their sponsors in the US Army, approached Starlink about cooperating on a project to make their low-Earth orbit constellation provide position, navigation, and timing capabilities. Although initially interested in the project, Starlink honcho [Elon Musk] put the brakes on things, leaving [Todd]’s team high and dry. Not to be dissuaded, they bought a Starlink user terminal, built what amounts to a small radiotelescope — although we’ve seen something similar done with just an RTL-SDR — and proceeded to reverse-engineer the structure of Starlink’s Ku-band downlink signal. The paper (PDF link) on their findings is densely packed with details, such as the fact that Starlink uses an orthogonal frequency-division multiplexing (OFDM) scheme.

It’s important to note that their goal was not to break encryption or sniff in on user data; rather, they wanted access to the synchronization and timing signals embedded in the Starlink data structures. By using this data along with the publically available ephemera for each satellite, it’s possible to quickly calculate the exact distance to multiple satellites and determine the receiver’s location to within 30 meters. It’s not as good as some GPS-Starlink hacks we’ve seen, but it’s still pretty good in a pinch. Besides, the reverse engineering work here is well worth a read.

Thanks to [Adrian] for the tip!

Universal music translation network

Hiding Data In Music Might Be The Key To Ditching Coffee Shop WiFi Passwords

In a move guaranteed to send audiophiles recoiling back into their sonically pristine caves, two doctoral students at ETH Zurich have come up with an interesting way to embed information into music. What sounds crazy about this is that they’re hiding data firmly in the audible spectrum from 9.8 kHz to 10 kHz. The question is, does it actually sound crazy? Not to our ears, playback remains surprisingly ok.

You can listen to a clip with and without the data on ETH’s site and see for yourself. As a brief example, here’s twelve seconds of the audio presenting two versions of the same clip. The first riff has no data, and the second riff has the encoded data.

You can probably convince yourself that there’s a difference, but it’s negligible. Even if we use a janky bandpass filter over the 8 kHz -10 kHz range to make the differences stand out, it’s not easy to differentiate what you’re hearing:

After many years of performing live music and dabbling in the recording studio, I’d describe the data-encoded clip as having a tinny feedback or a weird reverb effect. However, you wouldn’t notice this in a track playing on the grocery store’s speaker. Continue reading “Hiding Data In Music Might Be The Key To Ditching Coffee Shop WiFi Passwords”