RECONSTRUCTION OF BAND LIMITED SIGNALS.

A signal, ft, bandlimited by frequency, omega, is completely defined by sample values taken at intervals of piomega. If the signal is unknown over some time interval greater than piomega, missing samples prevent synthesis by ordinary means. A method for rebuilding incomplete waveforms by repeated synthesis using sample values taken in excess of band width requirements is shown to converge and is demonstrated with selected functions. Closed form methods follow from the repeated sampling scheme and provide reconstructions with limited calculations and improved accuracy. A minimum sample technique proves to be most useful in terms of calculations and accuracy when applied to a real waveform. Errors for aliasing, truncation and measurement affect the accuracy of the solutions, and their relations to practical limits on reconstruction are derived. Author