This paper is concerned with finite sections of convolution type operators defined on cones, whose symbol is the Fourier transform of an integrable function on R-2. The algebra of these finite sections satisfies a set of axioms (standard model) that ensures some asymptotic properties like the convergence of the condition numbers, singular values, epsilon-pseudospectrum and also gives a relation between the singular values of an approximation sequence and the kernel dimensions of a set of associated operators. This approach furnishes a method to determine whether a Fredhohn convolution operator on a cone is invertible. (C) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.