Undoing convolution in nature

Prediction-error filtering is also called ``deconvolution''. This word goes back to very basic models and concepts. In this model one envisions a random white-spectrum excitation function $\bold x$existing in nature, and this excitation function is somehow filtered by unknown natural processes, with a filter operator $\bold B$producing an output $\bold y$ in nature that becomes the input $\bold y$to our computer programs. This is sketched in Figure .

 

systems Figure 1 Flow of information from nature, to observation, into computer.

Then we design a prediction-error filter $\bold A$ on $\bold y$,which yields a white-spectrumed output residual $\bold r$.Because $\bold r$ and $\bold x$ theoretically have the same spectrum, the tantalizing prospect is that maybe $\bold r$ equals $\bold x$,meaning that the PEF $\bold A$ has deconvolved the unknown convolution $\bold B$.