L-I-M, as I understand your RADAR description, the carrier was sinusoidal -- linearly frequency-swept (modulated) over a 1MHz range by a 1KHz "sawtooth" signal. Every millisecond, the modulation frequency would reach peak, then instantly drop back 1 MHz, and begin its sweep again... (IOW, I'd guess that early RADARs were modulated by a VCO -- driven by a relaxation oscillator-generated sawtooth...)
OTOH, a point source on a rapidly-spinning sphere -- Doppler-modulated by the angular velocity -- would sinusoidally reach a peak frequency, and sinusoidally drop back to minimum. Then, with the signal occluded by the object, the signal would be attenuated (below detectable level) for half a revolution, and then the half-sinewave signal would reappear. (Basically a frequency-modulated signal, driven by a half-rectified sine wave...)
Going to go "bomb" my bandwidth allocation, watch the video, hope for a look at the actual signal, and -- I hope -- stop speculating... '-)
Back soon...
Your understanding of LFM is spot on. Originally LFM used a dispersive delay line, with delay proportional to frequency to modulate the signal. Virtually all modern radar systems use digital waveform generators, and multiplier chains.
https://en.wikipedia.org/wiki/Chirp
I would call it both amplitude and frequency modulated...
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Well, there you have it, folks -- have at it! '-)