Zero-crossing analysis - rapid bat identification
Although analog bat detectors are still widely used for identifying bats in the field acoustically, visual analysis of sonar pulse frequency characteristics can be more reliable and requre less skill. However, in a small field instrument with little computing power, FFT plots can be fuzzy and 'smeared' (see here), whereas a zero-crossing (ZX) computation is faster and more compact, producing clearer results without the distraction of harmonics.
Ultra Sound Advice has developed an efficient ZX algorithm which calculates the frequency of the strongest component with an accuracy of 1 part in 240 (eg 0.25 kHz at 60 kHz), yet requires less than 30 digital samples. For a given sampling rate, this considerably reduces the 'smearing' effects, enabling the characteristic shapes of rapid bat sonar transients to be displayed with remarkably high definition. It is often possible, simply by inspection of the ZX plot, to distinguish between individual bats of the same species operating at very slightly different sonar frequencies.
This efficient ZX algorithm and visual display is an excellent method of identifying bat sonar in the field.
Examples of displays using this algorithm are shown in the bat sonar gallery, demonstrating fine detail, accurate frequency definition and tolerance to gross amplitude variations.
Signal sampling rate
Fast signal digitising rates are essential for serious bat sonar analysis. The Nyquist criterion (sampling speed must be at least twice the maximum signal frequency) is not applicable to 'non-stationary' bat sonar with steep FM sweeps, where much higher sampling rates are essential to avoid 'smearing'.
This picture shows two pulses taken from a "feeding buzz" of a common pipistrelle. The signal starts at 100 kHz and falls to 45 kHz in 1.2 ms.
A typical signal sampling rate of say 400 kS/s, and an FFT processing size of say 256 points, would tend to "smear" the entire pulse. But here, a zero-crossing algorithm with only 30 points produces a clean, precise frequency plot.
In this version, the frequency plot is inverted into period, producing a straight line. The bat is using a hyperbolic frequency sweep, which maximises target range accuracy by eliminating Doppler ranging errors. (Cursors show frequencies).
Some constant-frequency bats (eg horseshoes) may also produce very short (< 2 ms) hyperbolic sweeps at each end of their long CF pulses.