reveals the QPO more clearly. Here we use the XWT introduced by @kel03.

After the continuous transform identifies that a periodic pattern exists in the data, the dilation that characterizes this period is obtained from the global wavelet power spectrum and is used to create a sinusoidal mock signal. The continuous wavelet transform coefficients of the data signal $f_{a}(t)$ are then multiplied by the complex conjugate of the continuous transform coefficients of a mock signal $f_{m}(t)$. The results are mapped out in wavelet space and analyzed for a correlation.

The cross-wavelet transform takes the form $$\widetilde f_{c} (l,t')= \widetilde f_a(l,t')\widetilde f^{*}_m(l,t')$$ where the continuous wavelet coefficients $\widetilde f_a$ and $\widetilde f_m$ are given by Equation \[coefficients\].

Figure \[sinecross\] shows the cross-wavelet for the same sinusoidal signal of varying frequency used in Figure \[sinecwt\]. The mock signal was calculated using the 6s period found in the wavelet power spectrum (see Fig. \[sinegwps\]) and as the concentrations in the real and power panels of Figure \[sinecross\] show, the cross-wavelet finds that this 6s period exists in the first half of the time series, illustrating the cross-wavelet’s ability to highlight a QPO.

The reader may refer to @kel03 for a full review of 