The physical principles and signal processing techniques underlying bat echolocation are investigated. It is shown, by calculation and simulation, how the measured echolocation performance of bats can be achieved.

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We outline the steps in this calculation as follows. The bat estimates η from the power S1,2 received in left and right ears: η̂=(S1−S2)/(S1+S2). The echo power for constant SNR is proportional to receiver gain: S1,2=(S+N)G1,2, assuming d≪R. Here S is the target power received at range R, and N is the noise power. From this the error Δη=η̂−η in estimating η, due to noise contaminating the signal, is determined. We substitute Δη into the right side of Eq. (7) and find Δθ as a function of θ. For realistic parameter values Δθ is insensitive to θ, as observed in Fig. 3. For a target of constant cross section, it is more realistic to hold the noise power constant than to say SNR is fixed, in which case S1,2=SG1,2+N. In this case the SNR is a maximum at θ=0, and decreases as θ increases. So from Fig. 4 we see that Δθ increases with θ.
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This is in theory the best resolution that can be attained for a signal of bandwidth B. In practice many FM bat species get very close to this resolution.
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Thus, for the terminal phase resolutions of Sec. VII we find that, if the bat images what it sees in front of it to a range of 1 m, then it must process 350 000 resolution cells 200 times per second.
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