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In my application I have to measure the transit-time of an ultrasonic signal
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Before jumping into implementing a counter to measure the round-trip distance, have you considered other options?
Radar and sonar systems transmit wide bandwidth signals as either chirps (swept frequencies) or pseudo-noise codes, and then cross-correlate the echos with the transmit code (this is called pulse compression). This results in an echo return with an impulse-like shape. You can detect the round trip distance via detecting that pulse, or you can Fourier transform and measure the phase slope.
FMCW radars (like the type the cops use to catch you speeding) transmit a chirp, mix the echo with the transmit signal, and the mixed signal can be used to determine the distance and speed of the target (something like that anyway ...)
Cheers,
Dave