  We shortly recall the mathematical and physical aspects of Talbot's
self-imaging effect occurring in near-field diffraction. In the rational
paraxial approximation, the Talbot images are formed at distances z=p/q, where
p and q are coprimes, and are superpositions of q equally spaced images of the
original binary transmission (Ronchi) grating. This interpretation offers the
possibility to express the Talbot effect through Gauss sums. Here, we pay
attention to the Talbot effect in the case of dispersion in optical fibers
presenting our considerations based on the close relationships of the
mathematical representations of diffraction and dispersion. Although dispersion
deals with continuous functions, such as gaussian and supergaussian pulses,
whereas in diffraction one frequently deals with discontinuous functions, the
mathematical correspondence enables one to characterize the Talbot effect in
the two cases with minor differences. In addition, we apply, for the first time
to our knowledge, the wavelet transform to the fractal Talbot effect in both
diffraction and fiber dispersion. In the first case, the self similar character
of the transverse paraxial field at irrational multiples of the Talbot distance
is confirmed, whereas in the second case it is shown that the field is not self
similar for supergaussian pulses. Finally, a high-precision measurement of
irrational distances employing the fractal index determined with the wavelet
transform is pointed out
