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This contribution deals with the design of a fully digital multi-rate receiver, operating on non-synchronized bandpass samples. Issues related to aliasing, sample rate conversion and timing correction are considered. We compare various receiver alternatives in terms of the BER degradation caused by aliasing and non-ideal timing correction. In particular, we focus on a low-complexity receiver performing sample rate conversion prior to matched filtering by means of an interpolator. We show that the BER degradation can be reduced to about 0.1 dB by careful selection of the system parameters, but at the expense of a large oversampling factor. A similar BER degradation can be achieved at a considerably smaller oversampling factor by including a simple digital anti-aliasing filter in front of the interpolator. We will develop a new type of anti-aliasing filter based on CIC filters. The distortion introduced by this CIC-type filter can be compensated for, by replacing the matched filter by an optimized receiver filter.