Useful analytical techniques for determining optimum signal parameter values in binary data communication over a channel corrupted by a combination of white Gaussian noise and impulsive noise are derived and presented in this dissertation. The analysis is based on a linear channel model and the optimality criterion used throughout is minimization of the decision error probability. A general expression for the probability of error is also obtained, based on the characteristic functions of the various noise and interference terms affecting the decision. Efficient numerical evaluation of this integral equation is made possible by the derivation of a suitable general expression for the characteristic function of the filtered impulsive noise component. Series expansions and a novel closed-form approximation of this characteristic function are also presented. The closed-form approximation applies to situations in which the composite response shaping the noise impulses is that of a Gaussian filter. This approximation yields the desired characteristic function with a maximum relative error of 0.5 percent. A common assumption in the analysis of impulsive noise channels is that at most one noise impulse occurs to affect a given decision. In practice this assumption is not always valid. However, in this work it is shown that optimum signal parameter values can be determined subject to the single noise impulse assumption and without regard to the white Gaussian noise component. The parameter values thus determined are optimum in a strict sense, with no restriction on the number of noise impulses that might actually occur to affect a given decision. Optimality tests based on the characteristic function of the filtered impulsive noise component are also derived. [...]