This thesis demonstrates how a Fast Gradient approximation to a Lattice Filter can be used as an Adaptive Line Enhancer for sampled data consisting of multiple switching tones in correlated noise. A tradeoff analysis is performed with four methods of digital filtering including a conventional Digital Fourier Transform (DFT) algorithm, a Least Mean Squares (LMS) adaptive algorithm, a Fast Recursive Least Squares (Fast RLS) adaptive algorithm, and the Fast Gradient adaptive algorithm. The DFT algorithm is incapable of removing correlations from the incoming noise, and the LMS and Fast RLS algorithms become unstable when a dynamic switching environment is being filtered. The Fast Gradient adaptive algorithm simulated on a computer is robust and capable of converging to an optimal set of FIR filter weights with minimum Mean Squared Error. Parameters for the Fast Gradient algorithm are optimized to provide good filter performance with a minimum number of computations. / Master of Science