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The miniaturization required for interfacing with the brain demands new methods of transforming neuron responses (spikes) into digital representations. The sparse nature of neural recordings is evident when represented in a shift invariant basis. Although a compressive sensing (CS) framework may seem suitable in reducing the data rates, we show that the time varying sparsity in the signals makes it difficult to apply. Furthermore, we present an adaptive sampling scheme which takes advantage of the local characteristics of the neural spike trains and electrocardiograms (ECG). In contrast to the global constraints imposed in CS our solution is sensitive to the local time structure of the input. The simplicity in the design of the integrate-and-fire (IF) make it a viable solution in current brain machine interfaces (BMI) and ambulatory cardiac monitoring.