Methods and devices for processing GPS signals are provided. The device includes: a memory for storing one or more lookup tables, each lookup table including a plurality of entries, each entry including an input segment and an output segment, wherein the output segment is a system response to the corresponding input segment. The device further includes a processor configured to receive an input data sequence including one or more input segments, and for each of the input segments, retrieve from one of the lookup tables the output segments corresponding to the input segment. The processor is further configured to perform a time-shifted sum of one or more output segments to produce an output sequence that is a downsampled representation of the input data sequence.