Today police use lasers, not radars, but who knows. They need precision in detection, also they need evidence for court, because of that they today include video and photo imaging tech.
I remember this circuit from a few years ago, lots of people try to build that.
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This is circuit decription :
"This circuit uses a 1458 dual op-amp to form a radar detector. C1 is the detector of the radar signal. The first op-amp forms a current-to-voltage converter and the second op-amp buffers the output to drive the piezo transducer. R5 sets the switching threshold of the second op-amp; normally it is adjusted so that the circuit barely triggers on background noise, then it's backed off a bit. The response of the circuit may be tuned by adjusting the length of the leads on C1. For typical road-radar systems, the input capacitor's leads should be about 0.5 to 0.6 inches long."