Despite the fact that engineers learn about the fact that
one should use the Dirac Delta (?function?) for the description
of time-invariant channels (linear systems, operators), or have to learn
the classification of signals into continuous and discrete, periodic
and non-periodic (and then decaying, say square integrable), one
must say that the mathematical theory describing ``signals''
and thus the operations on them (e.g.\ signal processing tasks)
is far from satisfactory from an applied viewpoint.

What about even slightly \tblue{time-varying signals}, like heart-beat,
or a piece of music (compressed using the MP3 algorithm), the
compression of images or other practical tasks. Which of the
mathematically well established function spaces are useful?