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Astron. Astrophys. 328, 670-681 (1997)

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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 ([FORMULA]) at [FORMULA] (Figs. 12 and 13).

We also examine the Morlet wavelet transform [FORMULA] for a harmonic (11-y period) signal exhibiting a 1-y phase shift ([FORMULA]) (Figs. 14 and (15).

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

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

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

[FIGURE] Fig. 15. Canonical example of a Morlet wavelet transform: the sinusoidal phase is shifted by [FORMULA]. 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).

[FIGURE] Fig. 16. Morlet wavelet transform for an artificial example: modulus of sinusoidal with a gap of two oscillations; modulus of wavelet coefficients.
[FIGURE] Fig. 17. Morlet wavelet transform for an artificial example: a sinusoidal with a gap of two oscillations; phase.
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© European Southern Observatory (ESO) 1997

Online publication: March 26, 1998

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