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.