This page has been under construction.


To be expanded sometime in the future.

Joint time-frequency analysis

What is a spectrogram?

Fourier analysis

Trade-off between time resolution and frequency resolution

spectrogram example

Time resolution vs. frequency resolution

Below I've shown the spectrogram of a single call from one of my own recordings. The program used is CoolEdit.
To illustrate the effect of varying window size, it plotted the spectrogram for various FFT sizes, using a Gaussian window:
16 frequency bands 32 frequency bands 64 frequency bands 128 frequency bands
The spectrogram for 16 bands has good time resolution (horizontal direction), but poor frequency resolution (vertical direction). Also the picture is very blocky. The spectrogram for 128 bands has good frequency resolution, but poor time resolution (it looks 'smeared' in the horizontal direction). Also note the 'noisy bits' in the picture, which are mostly vertical for the 16-band spectrogram and mostly horizontal in the 128-band spectrogram.
The spectrograms for 32 and 64 bands give the best of both worlds, fair time and fair frequency resolution, but are still quite blocky.

How do we remove the blockiness?

The answer is simple: use a bigger FFT, but keep the window size small !!!
Fortunately, Cooledit allows us to use a window function that is smaller than the FFT size. For example, a 256-band spectogram with a 25% window size has the same time and frequency resolution as a 64-band spectrogram with a 100% window size, but it is not blocky at all!
256-band spectrogram, window size 25% 64-band spectrogram, window size 100%

Two conclusions can be drawn from these pictures:

free bat call analysis software

There's a lot of places on the net about sound analysis, here are just a few of them:
This page was last updated August 7th, 2005