# Ultra High definition spectrograms

The frequency resolution of the bitmap spectrograms shown in the Bat sonar gallery is limited by the 240 pixel count of the analyser LCD. The calculations are actually carried out to much higher precision, as revealed by the spectrograms below - extracts of sonar from CF (constant frequency) bats.

Here, the frequency scales are magnified by fifty times to 20 Hz/pixel, except for Dusky leaf-nosed which is 100 Hz/pixel.

DFT sample lengths are only 64, except for Greater horseshoe[2], which is 256.

“Doppler confusion” is a short section of the Lesser horseshoe (2) spectrogram from the Bat sonar gallery, with vertical frequency scale magnified 50 times (20 Hz/pixel). The microphone receives sonar simultaneously from the moving bat and from reflections off a nearby wall. Interference of the 2 signals, Doppler-shifted by different amounts, results in low-frequency amplitude modulation. The DFT algorithm is confused while computing 2 nearly identical frequencies and produces cusp-shaped frequency plots synchronised with this modulation.

It is quite likely that the bat is also confused !

These "phase integrated" DFT spectrograms are a huge improvement in both frequency and time resolution compared to conventional DFT plots, but are still some way off theoretical limits, due to quantisation effects (with only 16-bit arithmetic) and signal noise - electronics, echoes, background.