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Electroencephalography (EEG) is a major tool for clinical diagnosis of neurological diseases and brain research. EEGs are often collected over numerous channels and trials, providing large data sets that require efficient collection and accurate compression. Compressive sensing (CS) emphasizing signal sparseness enables the reconstruction of signals from a small set of measurements, at the expense of computationally complex reconstruction algorithms. In this paper we show that using Discrete Prolate Spheroidal Sequences, rather than sine functions, it is possible to derive a sampling and reconstruction method which is similar to CS. Assuming non-uniform sampling our procedure can be connected with compressive sensing without complex reconstruction methods.