Useful Informative Signals
In the context of information theory:
Only signals exhibiting specific random characteristics have the capacity to transmit information effectively.
Moreover, it is the less probable data within these signals that carries a greater payload of information, aligning with the probabilistic nature of information theory.
Natural signals, such as sound or natural images, are more or less unpredictable in nature.
Therefore, deterministic mathematical models are unsuitable for representing informative signals.
On the other hand, these random informative signals may not be integrable (or summable), implying the non-existence of the Fourier integral.