Wavelet Transform, Frequency and Scale.

Cuthbert Nyack

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 coincide. 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 appear:-

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