Feature enhancement: pulsing

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Feature enhancement: pulsing

A sharp contrast is seen between the `crowded' energy map of the modulated oscillations (individual minima and maxima of the signal identified by the Mexican hat wavelet) in section 13 and and the `smooth' presentation of the norm-Morlet transforms of the same data in section 15. It may be of interest to keep the emphasis on individual events forming a sustained `wavetrain', but without assuming that the wavetrain is periodic. This can be achieved by the following simple algorithm:

  1. construct an energy map based on individual events.
  2. smooth the map by merging the events that are `close enough' to each other. This is achieved by scale-dependent filtering, in which the filter size is proportional to the wavelet size.
The result of these operations (Mexican hat wavelet and Gaussian filter) is shown on the following figures (20-22).

Figure 20: Smoothed energy map of can be compared to the Morlet-transform.

Figure 21: Smoothed energy map of the modulated oscillation.

Figure 22: Smoothed energy map of the intermittent signal.

Differences with Figs 17-19 are seen in the vertical spread of the contours, with better spectral localization using the locally-periodic Morlet wavelet, and in the horizontal spread -- particularly for the modulated wave -- where single events can contribute.

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Jacques Lewalle
Mon Nov 13 10:51:25 EST 1995