Successive projections-like algorithms for signal approximation/zero-error modelling

We show how successive projection-like algorithms may be used for approximation or exact modelling of a signal. For this purpose, we propose a new efficient algorithm providing adequate linear difference equations satisfied by the original signal. The projection operators at each step of the approximation algorithm and the new procedure are shown to be orthogonal. Finally, a pyramidal structure summarises the possibilities offered by the combinations of both procedures