Astron. Astrophys. 328, 670-681 (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 (11-y period) signal with a relatively small frequency change () at (Figs. 12 and 13).

We also examine the Morlet wavelet transform for a harmonic (11-y period) signal exhibiting a 1-y 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 minimum-type 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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