# Sonograms

Written by Paul Bourke

January 1998

A sonogram is a means of displaying both time and frequency information
at once, as opposed to a single FFT which displays the frequency spectrum
of a whole time series. Sonograms have found applications in many areas
but are particularly useful in the analysis of speech where the changing
frequency content of the signal is of primary interest.

Calculating a sonogram involves computing many short FFT's over the
time interval of interest.
In order to create smooth transitions in time and form an image of
reasonable width the short FFT segments overlap. Typically the overlap
is at least 50% and often up to 90%.
The magnitude or power of each of
these FFT's are "stacked" vertically generating a 2D display, ie: an image.

The magnitude of each Fourier component is mapped
onto a colour ramp, usually the blue through green to red ramp is used
where blue represents low values and red represents high values.

There is a trade-off between time and frequency resolution, as the FFT
window width is decreased the time resolution increases but the frequency
resolution decreases and visa versa (increasing the frequency resolution
by increasing the FFT window width decreases the time resolution).

### Example

The following shows a time series segment of 2048 points, a recording
from human EEG.
The following is the sonogram for the above time series.
The discrete nature along the frequency axis is controlled by the width
of the FFT window, in this case it is 128 samples, since the sampling
frequency is 500Hz this results in a frequency resolution of about 3.9Hz.
In addition, the high DC component (signal mean) is removed for scaling
purposes.

A more unusual method of displaying the sonogram is as a 3D surface with
the magnitude (or power) of the frequency components proportional to the
height of the surface. The 3D representation of the above sonogram is
illustrated below.

This does not contain any more information than the more conventional
2D sonogram but the structure is generally easier to appreciate.