up as a pattern over all translations at a specific dilation.

By way of example, Figure \[sinecwt\] shows the real part and the power of the continuous wavelet transform (second and bottom panel, respectively) for a sinusoidal signal of varying frequency (top panel). Here, the real part of the transform shows oscillatory behavior corresponding to the two periodicities of the sinusoidal signal at dilations of 3s and 6s with a break in translation at 50s corresponding to the time where the change in frequency occurs. The bottom panel in Figure \[sinecwt\] shows that the power of the continuous wavelet transform is concentrated at these two frequencies as well.

The hatched area in both panels of Figure \[sinecwt\] represents the cone of influence: the region where edge effects become important. It arises because discontinuities at the beginning and end of a finite time series result in a decrease in the wavelet coefficient power. Also shown in the header of Figure \[sinecwt\] are the number of dilations used ($N_l$) and the ranges of dilations explored. We discuss $\alpha$ and the normalization of Figure \[sinecwt\] in the following section.

### Significance Tests {#sigtestsection}

Significance tests can be created for the continuous wavelet transform 