The uniform sampling rate required to reconstruct a deterministic bandpass signal x(t) having spectrum confined to I1∪I2, where I1 = [−ω0−σ/2, −ω0+σ/2), I2 = [ω0−σ/2, ω0+σ/2) with ω0?σ/2≳0 depends critically on the positioning of the band and varies from σ/π to 2σ/π samples per second, the minimum rate of σ/π being attained if and only if ω0+σ/2 is an integer multiple of σ. If the bandpass signal x is now used as a common input to an even number m of linear time-invariant filters to produce m outputs z1(t),...,zm(t), then it is proved that, under a certain ’’independence’’ requirement on the filters (a matrix function condition), the input x may be reconstructed from samples of the outputs {zk(t)}, each output being sampled at the uniform rate of σ/mπ samples/second, or (1/m)th the minimum sampling rate associated with the input. The dependence on band position is removed by a partitioning of the set I1∪I2 into m disjoint subsets J1,...,Jm of equal length and a subsequent mapping procedure which allows J1 to be mapped (discontinuously) in a one-to-one manner onto Jk for 1?k?m. As an example, it is shown that samples of the bandpass signal x and its first derivative x′, taken at the common rate of σ/2π samples per second (m = 2), suffice to determine x completely, a generalization of an early theorem due to Fogel [IRE Trans. Inf. Theory, IT-1, 47–48 (1955)].