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.