The Prony method for approximating signals comprising sinusoidal/exponential components is known through the pioneering work of Prony in his seminal dissertation in the year 1795. However, the Prony method saw the light of real world application only upon the advent of the computational era, which made feasible the extensive numerical intricacies and labor which the method demands inherently. The Adaptive LMS Filter which has been the most pervasive method for signal filtration and approximation since its inception in 1965 does not provide a consistently assured level of highly precise results as the extended experiment in this work proves. As a remedy this study improvises upon the Prony method by observing that a better (more precise) computational approximation can be obtained under the premise that adjustment can be made for computational error , in the autoregressive model setup in the initial step of the Prony computation itself. This adjustment is in proportion to the deviation of the coefficients in the same autoregressive model. The results obtained by this improvisation live up to the expectations of obtaining consistency and higher value in the precision of the output (recovered signal) approximations as shown in this current work and as compared with the results obtained using the Adaptive LMS Filter.