High resolution bat sonar analysis

Full-spectrum analysis of bat sonar typically makes use of short-time discrete Fourier transforms (STFT, more commonly known as DFT). There are several alternative analysis methods, but none are as generally robust with short time-varying signals, or as computationally efficient, as DFT. [Zero-crossing analysis can be a useful tool for identification, but all harmonic information is discarded.] The digitised ultrasound signal is analysed by DFT in short samples, and the result is a frequency vs. time spectrogram. For DFT the frequency resolution is roughly 1 part in N (the sample size). Frequency resolution can be refined by increasing the length of the sample, but the sample is then acquired, and therefore averaged, over a longer time. Furthermore, processing time increases proportionally to Nlog2N. Faster A-to-D converters improve time resolution, but at the expense of higher power consumption (important in hand-held devices), lower frequency resolution (as sampling rate increases) and larger data files.

Typically, bat sonar is analysed with DFT sample sizes of 256 or more, and sampling rates of up to 400 kS/s, resulting in spectrogram frequency resolutions of about a kHz, and a time resolution of around a millisecond. This is barely sufficient for looking at sonar from many European and US bats, but seriously inadequate for detailed examination of sonar from many tropical and European bats with sonar sweeps and/or feeding buzz pulses of less than a millisecond.

Standard DFT algorithms discard phase information, but by re-introducing it, dramatic improvements in time and frequency resolution are possible, and DFT sample size can be  reduced. For instance, a 64-point DFT incorporating this “phase integrated” technique can yield frequency and time resolutions better than 0.08 kHz and 50 µs (with a 12-bit AtoD converter sampling at 600 kS/s). Surprisingly, this technique has been ignored by bat researchers, although it has been applied in other research fields for over 50 years.

The bat sonar gallery shows spectrograms produced by PISA, a hand-held analyser manufactured by Ultra Sound Advice, which uses this technique. Here the frequency resolution is limited by the 320x240 pixel screen, but much more detail can be revealed by expanding the frequency scale (see HD spectrograms) or transferring data to Excel (see HD Excel spectrograms).

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