Sampling Bandpass Signals

In a recent paper [1], Brown examined the sampling of a real finiteenergy bandpass signal having an (angular) bandwidth ¿ (in radians per second) at the theoretically minimum (average) rate of ¿/¿ samples per second. Following Grace and Pitt´s [2] quadrature sampling, a particular case of Kohlenberg´s second-order sampling [3, 4], Brown has proved the feasibility of a separate interpolation of the in-phase and quadrature components of the signal when ¿o = k¿/2 (Brown´s condition), where ¿o is the center (angular) frequency of the signal and k is an arbitrary positive integer. Here the problem is reconsidered from a general point of view, introducing, under Brown´s condition, an interpolation formula which includes that of Grace and Pitt and which extends a theorem of Populis [5-7]. We indicate the necessary and sufficient conditions to obtain a separate interpolation, offering closed formulas to obtain the interpolation functions. We also discuss the minimum oversampling rate needed whenBrown´s condition is not verified.