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 existing in nature, and this excitation function is somehow filtered by unknown natural processes, with a filter operator producing an output in nature that becomes the input to our computer programs. This is sketched in Figure 1.

 

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

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