In this letter, we propose a new approach to reconfigurable receivers using random acquisition techniques. Random projections have been widely used within the context of compressive sensing for sub-Nyquist signal acquisition. In the system we propose, we design the random sensing signals so as to filter undesired components in the signal and result in measurements equivalent to those obtained had the signal been filtered prior to acquisition. Because the random signals are digitally generated, the system is reconfigurable; the signal's components to be filtered can be changed by changing the digitally generated random signals. The system digitizes the measurements at a rate proportional to the desired bandwidth only, not the total signal bandwidth.