In a recent work [1], we developed and analyzed a classifier for multiple M-ary Frequency Shift Keying (MFSK) signals that traveled over a static frequency non-selective Rayleigh fading channel and are contaminated with additive white Gaussian noise. In this paper, we extend the classifier to the case in which the MFSK signals traveled over a time varying flat correlated fading channel and contaminated with impulsive noise. Specifically, the considered impulsive noise is the Middelton's class A noise model. The classifier is based on approximating the likelihood function (LF) of the received signal. We use complex envelope representation of the signals and noise to derive the likelihood function. The Karhunen-Loeve expansion is used to have a more precise description of the fading process. Simulation experiments are illustrated to evaluate the performance of the classifier and to validate the theoretical developments.