About Bi-periodic Samplings

To superpose delayed samplings with a unique period is a worthwhile technique. The first contribution in this domain comes from J.L. Yen, half a century ago, and improvements were due to A. N. Papoulis theorem and J. R. Higgins who proved that functions with energy spectrum in subbands can be recovered by samplings with same periods and with lags. In this paper, we study the case of two periodic samplings with equal or different periods, rational or irrational between them. This kind of sampling is natural in systems where the Doppler effect acts. The best linear estimation in the meansquare sense is given under an integral form. Solutions can be analytically obtained, for example, when the power spectrum is distributed in few bands or when the sampling periods are multiples.