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Bats use echolocation to navigate three dimensional obstacles while locating, identifying, and engaging targets. A theory is offered of image processing during the search and navigation phase of echolocation that uses Doppler frequency shifts. The information in frequency changes across the angle of elevation can be used to generate a three dimensional model of the environment when combined with the timing and the relative amplitude of the returned signals. The mathematics of frequency shifts for an emitter traveling at a large fraction of the velocity of propagation () is presented. Reported behavior that can be explained by this phenomenon is discussed.


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