Methods and devices for processing GPS signals are provided. The device includes: means for storing one or more lookup tables, each lookup table comprising a plurality of entries, each entry comprising an input segment and an output segment, wherein the output segment is a system response to the corresponding input segment; and processing means for receiving an input data sequence comprising 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, wherein the processing means 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.