This paper considers the reconstruction of digital complex baseband signals from M-periodically nonuniformly sampled real bandpass signals. With such a sampling, bandpass signals with arbitrary frequency locations can be sampled and reconstructed, as opposed to uniform sampling which requires the signal to be within one of the Nyquist bands. It is shown how the reconstruction can be carried out via an M-periodic time-varying finite-length impulse response (FIR) filter or, equivalently, a set of M time-invariant FIR filters. Then, a least-squares design method is proposed in which the M filter impulse responses are computed in closed form. This offers minimal filter orders for a given desired bandwidth. This is an advantage over an existing technique where ideal filters are first derived (ensuring perfect reconstruction) and then windowed and truncated, which leads to suboptimal filters and thus higher filter orders and implementation complexity. A design example illustrates the efficiency of the proposed design technique.