Time Domain Auto Pulse Shaping Operation

In this paper, a time domain pulse shaping operation is presented. The proposed operation transforms the given time limited, positive amplitude, finite energy and even-symmetric pulse into a pulse that has an increased duration for its constant maximum amplitude while maintaining the same time spacing between instants of zero amplitude levels as the original pulse. If the given pulse amplitude decreases monotonically, the transformed pulse is characterized by an increase in the duration for the maximum constant amplitude portion and an increase in the duration of monotonically decreasing amplitude portion. The proposed operation involves multiplying the given pulse with a positive dc shifted version of the mirror image of the pulse, the image being taken around time axis and the amount of shift being equal to twice the peak amplitude of the pulse under consideration. The proposed operation is applied to Gaussian pulse, triangular pulse, raised cosine pulse and pulses derived from error functions and Gaussian pulses. When the proposed operation is applied recursively, the given pulse, irrespective of its original shape, transforms into a rectangular pulse. With each application of the said operation, the pulse energy increases reaching a value that is equal to that of a rectangular pulse.