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Although recent advances in neuroscience, information technology and microelectronics have enabled implanting miniature and highly intelligent devices within the brain for in vitro diagnostic and therapeutic functions, novel signal processing methods are required for energy efficient data acquisition due to power constraints accompanying these miniature devices. We present a new method for signal acquisition in brain implants based on Asynchronous Sigma Delta Modulators (ASDM) which requires less power than conventional methods. We also present a computationally efficient signal reconstruction algorithm using the time codes from the output signal of ASDM. Our method and algorithm are validated using subdural EEG signals recorded from an epilepsy patient.