The usefulness of wavelet analysis is demonstrated by considering analytica
l expressions for phase mixed Alfven waves in different physical circumstan
ces. The wavelet analysis is briefly introduced, using the complex-valued M
orlet wavelet, consisting of a plane wave modulated by a Gaussian, as the b
asic wavelet. The time and scale resolution of the wavelet transform are th
en discussed in more detail, by working out the transform of simple harmoni
c functions analytically. As an illustration of the power of wavelet analys
is, phase mixed Alfven waves are investigated. A comparison is made between
a truly finite harmonic wave and an Alfven wave, dissipated by phase mixin
g and, using the wavelet transform, it is demonstrated that it is possible
to distinguish between these two 'finite' signals. It is also possible to e
xtract the value of the dissipation coefficient from the wavelet transform.
When considering phase mixing of Alfven waves in a gravitationally stratif
ied atmosphere, the lengthening of the wavelengths is clearly evident in th
e transform, which provides an independent estimate of the value of the pre
ssure scale height. In a radially diverging atmosphere, the shortening of t
he wavelengths is also apparent in the wavelet transform, showing how the A
lfven speed varies along the loop and thus providing information on the cor
onal density and magnetic field. When applying wavelet analysis to observed
wavelike oscillations, it should be possible to infer properties of the co
ronal plasma by making a detailed study of the wavelet transform.