Summability methods are a useful tool in dealing with the problems in the soft computing like in filtering of the signals and for stabilizing the systems. Signals can be in the form of various types of series (Infinite Series, Fourier series, etc.) and hence, summability theory is applicable in finding the error of approximation and degree of approximation of such signals. In this chapter, the authors gave an introductory discussion on summability theory and approximation of the signals. Further, they explained about the stability of the frequency response of the system. Also, they used the Fourier approximation in the soft computing models (multilayer perceptrons; radial basis function (RBF) or regularization networks, and fuzzy logic models) and found the output data of requirement.