Spectrogram

Spectrograms are used extensively in the fields of music, linguistics, sonar, radar, speech processing,[1] seismology, ornithology, and others.

Spectrograms of audio can be used to identify spoken words phonetically, and to analyse the various calls of animals.

[2] A spectrogram is usually depicted as a heat map, i.e., as an image with the intensity shown by varying the colour or brightness.

There are many variations of format: sometimes the vertical and horizontal axes are switched, so time runs up and down; sometimes as a waterfall plot where the amplitude is represented by height of a 3D surface instead of color or intensity.

This process essentially corresponds to computing the squared magnitude of the short-time Fourier transform (STFT) of the signal

[5] From the formula above, it appears that a spectrogram contains no information about the exact, or even approximate, phase of the signal that it represents.

A smaller (shorter) window will produce more accurate results in timing, at the expense of precision of frequency representation.

This is an instance of the Heisenberg uncertainty principle, that the product of the precision in two conjugate variables is greater than or equal to a constant (B*T>=1 in the usual notation).