We do not address discretization issues in this paper.
However, it is worth noting, that in practice, we generally wish to
compute the chirplet transform of a discrete-time signal, and it
is sometimes the case that the mother chirplet is also discrete-time
and has no closed-form mathematical description.
Thus, *dilation* would require resampling, and *contraction*
would require antialiasing. In this case, the largest subspace we might
obtain would be the subspace that omits both dilation and tiling-size,
leaving us with the four-dimensional parameter space:

**S**_t_c,f_c,0,c,d \!=\!

C_t_c,f_c,0,c,d \: g \: \: s \!

Thu Jan 8 19:50:27 EST 1998