... The concepts of Fourier frequency and wavelet duration are obviously related. ... Among many sensible definitions, we chose to require that the peak of the wavelet mean spectrum should be matched with the singularity of the Fourier transform of the cosine wave. Then, it can be shown that the frequency of the cosine is related to the wavelet duration by the relation . ... The ambiguous definition of the duration of an event is common to the sizing of any object of irregular shape. ...