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This brief considers the problem of reconstructing a band-limited signal from its two-periodic nonuniformly spaced samples. We propose a novel reconstruction system where a finite-impulse response filter designed as differentiator followed by a time-varying multiplier recovers the uniformly spaced from the nonuniformly spaced samples. The system roughly doubles the signal-to-noise ratio with relatively few filter coefficients. The main advantage is that once the differentiator has been designed, it can be implemented with fixed multipliers, and only the coefficients of the time-varying multiplier have to be adapted when the sampling pattern changes; this reduces implementation costs substantially. In addition, the system allows an efficient polyphase implementation.