Systems and methods for converting wideband signals into the digital domain are provided herein. The system may include an electronic or guided-wave optic based replicator configured to obtain at least M replicas of a signal applied thereto, and an electronic or guided-wave optic based segmenter configured to segment a signal applied thereto into at least N segments based on time or wavelength. Together, the replicator and the segmenter obtain M×N segment replicas of the received signal. An electronic or guided-wave optic based mixer is configured to multiply the M×N segment replicas by a mixing matrix having dimension M×N and then to form M integrations each of N segment replicas so as to obtain a measurement vector of length M. A signal recovery processor is configured to obtain a digital representation of the received signal based on the measurement vector and the mixing matrix.