fs = 192 000 samples / second

Radio from Samples

Four transmitters, one road, one antenna. The receiver gets a single stream of numbers and has to find the music in it. Every sound you hear is demodulated from those samples, live.

Volume

0 antenna samples computed

Build the radio

Each layer fixes a problem the one before it can't.

Problem

Invention

Try this

The band

Waterfall of the antenna samples, 0 to 96 kHz. Click or drag to tune.

76.0kHzFM

The road

Drag the car, or focus the map and use the arrow keys. Both towers run an AM and an FM station; the two FM stations share 76 kHz.

At the antenna

WEST

EAST

Filter output–

Receiver gain–

On the speaker

Measured by correlating the speaker output with each transmitter's program. A check on the result; the receiver never sees these.

Inside the radio

››

Before the filter

After the filter

What is computed, and what isn't

Programs. Four programs are synthesized at 48 kHz: a plucked melody (WEST AM), a time signal with Morse call sign (EAST AM), a chord pad (WEST FM), a drum machine (EAST FM).
Transmitters. Each program is zero-stuffed to 192 kHz and band-limited (3 kHz AM, 5 kHz FM with 2.1 kHz pre-emphasis). AM: (1 + 0.85·m)·cos φ. FM: phase advances by 2π(f_c + 7 kHz·m)/f_s every sample.
The road. Each tower's signal falls as distance^−1.3. Fading adds a slow two-path interference pattern. Static is Gaussian noise added to every antenna sample.
The receiver sees only the antenna samples. Tuned circuits and the preselector are biquad resonators; the IF filter is a 191-tap Kaiser FIR; the envelope detector is a diode charging a 30 µs RC; the limiter is z/|z|; the discriminator is −Re(z[n]·z*[n−1]).
Audio leaves the detector, is low-passed and decimated to 48 kHz, and is played exactly as computed. Nothing is looked up or crossfaded.
The display reads the same buffers: the waterfall and spectra are 2048-point FFTs of the actual stages, and the zoom view evaluates the filter sum on the very samples that went into it.

Where this came from

Proof of Invention · prompt #124809 · radio · all out

start from individual radio-frequency samples and build a radio from scratch, entirely in code. design each layer on top of the last: AM transmitters, a band-pass filter, an envelope detector, a heterodyne mixer, automatic gain control, FM transmitters, an amplitude limiter, an FM discriminator, and an FM radio that snaps to the stronger of two stations. everything has to be real, every sound has to be demodulated from your samples, not a station lookup pretending. show it on a spectrum waterfall and let me drive between two stations, then zoom from the radio down through the filter into the samples while it runs. beside it, keep the spectrum before and after the filter. treat it like you're proving you could have invented radio yourself. go all out.

Built by Claude from this prompt. The prompt was written by Proof of Invention, a prompt machine with no language model inside: every sentence comes from a gene you can point to, and the same number gives the same prompt forever. The machine opens soon. Follow the build in Digital Renaissance · @0xsarac · a NeuraByte Labs experiment.