Conclusion

For didactic reasons, this article on random functions is based on a scientific approach close to the application, and more specifically on signal processing. Nevertheless, it should be borne in mind that random functions derive from much more fundamental concepts that the reader will find in mathematics textbooks, some of which are listed as bibliographical references [Doc. R 220v2].

To confine this conclusion to the initial applied framework, we'll try to focus it on an issue that has been overlooked throughout the presentation, namely the extremely blurred isthmus between a random and a highly correlated signal.

Let's imagine an experiment to measure the sound emitted by the waterfall of a copiously fed cascade. Clearly, measuring the noise in the waterfall's natural environment should yield a purely random signal. In other words, the...