A signal is temporally compressively sampled. A plurality of analog to digital converters are assembled to sample the signal. Each analog to digital converter of the plurality of analog to digital converters is configured to sample the signal at a time step determined by a temporal sampling function. The signal is sampled over a period of time using the plurality of analog to digital converters. Each analog to digital converter of the plurality of analog to digital converters produces a measurement resulting in a number of measurements for the period of time. A number of estimated signal values are calculated from the number of measurements and the temporal sampling function. The temporal sampling function is selected so that the number of measurements is less than the number of estimated signal values.