Abstract: A data receiving system for digital data communication described which uses asynchronous sampling and lagrangian or prolate spheroidal function interpolation on the received signal. A received analog signal is first asynchronously sampled, digitized stored in a memory and then processed using interpolation technique to recover the correct symbol timing of the symbols in the digitized data. The minimum sampling rate commensurate with channel band width is used. The correct symbol timing is continuously adjusted within certain pre-determined limits of the interpolation interval using a "jumping" algorithm which permits continuous symbol tracking. The recovered symbols are then equalized to compensate for channel distortion and decoded to give the originally encoded data. When bursts of data are being transmitted the data stored in memory is replayed to ensure that all data in the data burst is used for communication and that there is no transmission overhead requiring extra symbols for synchronization.