# Analysis of bat sonar

Full-spectrum analysis of ultrasound signals is typically carried out by using short-time discrete Fourier transforms (STFT), which are efficient and fast. The acquired digitised ultrasound signal is divided into short samples, and STFT is applied to each sample in turn. The resolution to which frequency can be determined is roughly 1 part in N (the sample size). Resolution can be improved by increasing the size of the sample, but then each sample is acquired over a longer time, and signals take longer to process (proportional to Nlog_{2}N). With rapidly-changing signals, the resulting STFT display becomes 'smeared' because the algorithm computes frequencies averaged over the time occupied by the sample.

This spectrogram shows a simple unprocessed spectral plot, where the individual STFT calculations for each sample and frequency 'bin' can be seen. To achieve better resolution, faster A-to-D converters can be used, but these consume more power, and produce large data files which take longer to store, process and display – not practical for battery-powered hand-held bat detector/data-loggers.

The resolution of STFT plots can be improved by

(a) overlapping a large number of smaller samples and averaging the results

(b) using phase information to calculate frequencies more precisely.

Dramatic improvements in spectrogram resolution are possible, although much greater computing power and speed is required compared to zero-crossing analysis.

If the aim is simply to identify bats rapidly in the field, then analysis of harmonics is not necessary, and simpler zero-crossing algorithms can be used.