Wavelet Transform, Frequency and Scale.
This applet shows one of the steps in producing a scalogram and
the relation between frequency and the wavelet parameters for the Gabor wavelet.
To produce one line of a scalogram,
the following equation is used:-
First ws(width and scale) and n(frequency) are set then the wavelet(both real and
imaginary parts) is correlated with
the signal and the correlation magnitude found. The wavelet is then translated in time and the process
repeated. After several repititions, the pink curve shown in the
applet is generated. This is repeated for different ws and the scalogram is built up.
To show the relation between wavelet parameters and frequency, ws is adjusted until it reaches a maximum for either signal burst. By
translating the wavelet using Tc, it is apparent that a maximum is
reached when the period of the signal and wavelet oscillations
As shown on the wavelet, the frequency in rad/s of the signal is
equal to 2*p*n/
ws for the Gabor wavelet.
This relation is valid provided both wavelet and signal burst are within the correlation
time domain when their peaks coincide.
When enabled, the following gif image show how the applet should
Return to main page
Return to page index
COPYRIGHT © 2007 Cuthbert Nyack.