Although the finite impulse response (FIR) Adaptive Line Enhancer (ALE) was developed in 1975 and has been used in a host of applications, no comprehensive performance analysis has been performed for this method, meaning no general equation exists for its signal-to-noise ratio (SNR) gain. Such an equation would provide practitioners an avenue for determining the amount of noise reduction the ALE provides for a particular application and would add to the general knowledge of adaptive filtering. Based on this motivation, this work derives the general equation for the FIR ALE SNR gain and verifies the equation through computer simulation, under the following assumptions: (1) A simplified Least Mean Squares (LMS) method is used for updating the embedded adaptive filter located within the ALE, (2) The received signal (i.e. the input signal to the ALE) is a summation of sinusoids buried in additive zero-mean white-Gaussian noise (AWGN), (3) The received signal is oversampled (i.e. the sampling rate is larger than the Nyquist rate), and (4) The ALE filter length is an integer multiple of the number of samples within one fundamental period of the original, noiseless signal.