This thesis is the presentation of an investigation into a classical bandlimited function extrapolation technique, namely the Papoulis-Gerchberg algorithm. This algorithm can be used in the field of RADAR signal processing to estimate the Time-Varying Target Density function of a moving target at different points in space in accordance with methods developed by Dr. Emre. The estimation of the Target Density function yields a scaled estimate of the effective cross-section of the target at that point. With all spatial points combined we would receive a picture of the target space at each time point. This would form, in effect, a real time image of the target space. The study consists of exploring the capabilities of the Papoulis-Gerchberg algorithm, thereby evaluating its possible use in the algorithm for estimating the Time-Varying Target Density function. The study also explores the effectiveness of the Papoulis-Gerchberg algorithm when applied to a bandlimited Target Density function. The two algorithms were simulated using MATLAB and the results were generated as comparisons between MATLAB charts.