Doppler shift calculator

What's going on

When a target moves towards the radar, each successive wavefront it reflects has slightly less distance to travel back. The reflected waves arrive bunched closer together — a higher frequency. Moving away stretches them out — a lower frequency. It's the same effect that makes a siren drop in pitch as it passes you, except the shift happens twice: once on the way to the target and once on the reflection. That's where the factor of 2 comes from:

The crucial detail is v_radial: only the part of the target's speed pointing along the radar's line of sight produces a shift. A target flying straight at the radar (θ = 0°) gives the full effect. One crossing perfectly side-on (θ = 90°) gives no Doppler shift at all, however fast it's going — for that instant, its range isn't changing. Drag the angle slider below and watch the radial component collapse.

The shifts are tiny compared with the carrier — a jet at 300 m/s seen by a 10 GHz radar shifts the echo by only about 20 kHz out of 10,000,000 kHz. Radar receivers measure it by comparing the echo against a copy of the transmitted signal, which is why coherent (phase-stable) transmitters matter so much.

Why you should care

Here is the problem Doppler solves. Point a radar at a low-flying aircraft and the echo from the aircraft arrives mixed with the echo from everything behind it — hills, buildings, the sea. That background clutter can be a million times stronger than the target. On range alone, the aircraft is invisible: a 2 m² echo buried inside a 2,000,000 m² one.

But the hillside isn't moving. Its echo comes back at exactly the transmitted frequency — zero Doppler — while the aircraft's echo comes back shifted. Put a filter in the receiver that rejects a narrow band around zero Doppler and the mountain vanishes, leaving the aircraft standing alone. This is moving target indication (MTI), and it's the single biggest reason Doppler matters: it doesn't just measure speed, it makes moving targets visible at all.

The same trick runs the modern world: weather radars map storm winds from the Doppler of raindrops, police radar and speed cameras are pure Doppler devices, and airborne radars use it to spot vehicles against the ground rushing past below.

Now connect it to the angle slider. A target crossing side-on has zero radial speed — zero Doppler — so its echo lands in exactly the band the clutter filter rejects. To an MTI radar, a crossing target looks like a hillside. Watch it happen in the spectrum below: drag θ toward 90° and the target line slides into the clutter notch and is eaten.