# Demo — Range-Doppler Map
The range-Doppler map is what a pulse-Doppler radar actually produces: a 2D picture with clutter piled up at zero Doppler and movers standing out in their own cells. This demo lets you move a target, toggle MTI, and find the blind speed where the target vanishes into the clutter notch.
## The picture
A target's Doppler shift is $f_d = 2 v_r / \lambda$. MTI cancels the zero-Doppler clutter but creates blind speeds at
$$
v_{\text{blind},n} = \frac{n\,\lambda\,\text{PRF}}{2}.
$$
A target whose velocity lands on a blind speed is cancelled along with the clutter.
## Interactive demo
Open in full screen
## Walkthrough
1. **Look at the default map.** A bright vertical ridge sits at zero Doppler (clutter); a single bright cell off the ridge is the moving target.
2. **Slide the target velocity.** The target cell slides along the Doppler axis while the clutter ridge stays fixed at zero — that separation is what makes the target detectable.
3. **Toggle MTI on.** The zero-Doppler column is nulled: the clutter ridge collapses and the target pops out against a clean background.
4. **Read the blind-speed readout.** With MTI on, set the target velocity to the first blind speed $v_{\text{blind},1}$. The target lands in the notch and **disappears** — cancelled with the clutter.
5. **Raise the PRF.** The blind speeds move higher; nudge the target off the notch and it reappears. This is exactly why pulse-Doppler radars favor higher PRF.
6. **Change the wavelength (band).** The Doppler-to-velocity scaling changes; the same Doppler shift now corresponds to a different velocity.
## Key observations
- **Clutter is rejected by Doppler, not amplitude.** It is far stronger than the target but lives at zero Doppler, so MTI nulls it without touching the mover.
- **Blind speeds are MTI's cost.** A target on a notch is invisible; PRF choice manages where the notches fall, trading against range ambiguity.
- **The B-21's motion is hard to hide.** Once moving, its Doppler signature stands off the clutter ridge — defeating this picture is what Block 2's EA techniques are for.
## Source
MATLAB · code/L5_DopplerMTI.m↓
The in-class script plots the single-delay MTI response $|H(f)| = 2|\sin(\pi f T)|$, marks the blind speeds, and builds a synthetic range-Doppler map before and after MTI.