Wavelet Analysis: the effect of varying basic wavelet parameters

The most commonly used methods to analyse ( observed) quasi-periodic signals are standard techniques such as Fourier and wavelet analysis. Whereas a Fourier transform provides information on the dominant frequencies, wavelet analysis has the added advantage of providing the time localisation of the various frequency components. The usefulness and robustness of wavelet analysis is investigated by varying the different parameters which characterise the 'mother' wavelet. We examine the effect of varying these parameters on the temporal and frequency resolution and the damping profile, which can be obtained from the wavelet transform. Additionally, the effect of a changing periodicity on the wavelet transform is investigated. Both simple harmonic functions and intensity oscillations observed by TRACE are used to demonstrate the various advantages and disadvantages of the different methods. In general, using the Paul wavelet or a smaller value of the wavelet parameter k provides a better time resolution, whereas the Morlet wavelet or a larger value of k improves the frequency resolution. Overall, our results indicate that great care is needed when using a wavelet analysis and that all the possible factors that could affect the transform should be taken into consideration.