Astron. Astrophys. 328, 670681 (1997)
Appendix
The most popular canonical example (see e.g. Farge, 1992) is a
frequency doubling in a harmonic signal. Here, we present the Morlet
wavelet transform of a harmonic (11y period) signal with a relatively
small frequency change () at
(Figs. 12 and
13).
We also examine the Morlet wavelet transform
for a harmonic (11y period) signal exhibiting a 1y phase shift
() (Figs. 14 and
(15).

Fig. 12. Canonical example of a Morlet wavelet transform: the sinusoidal period increases from 11 to 12 years. Modulus


Fig. 13. Canonical example of a Morlet wavelet transform: the sinusoidal period increases from 11 to 12 years. Phase


Fig. 14. Canonical example of a Morlet wavelet transform: the sinusoidal phase is shifted by . Modulus


Fig. 15. Canonical example of a Morlet wavelet transform: the sinusoidal phase is shifted by . Phase.

The third canonical example aims at illustrating Maunder
minimumtype events. For that, we examine the modulus of a periodic
signal that contains a gap of two oscillations (Figs. 16 and
17).

Fig. 16. Morlet wavelet transform for an artificial example: modulus of sinusoidal with a gap of two oscillations; modulus of wavelet coefficients.


Fig. 17. Morlet wavelet transform for an artificial example: a sinusoidal with a gap of two oscillations; phase.

© European Southern Observatory (ESO) 1997
Online publication: March 26, 1998
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