This report describes a polynomial design algorithm for linear residual generation for stochastic systems in both continuous and discrete time. It is shown how the two main steps in the design algorithm is extraction of a polynomial basis for the left null-space of a polynomial matrix followed by a J-spectral co-factorization of a para-hermitian polynomial matrix. For both these operations there exists good numerical tools. The design algorithm is successfully demonstrated on a number of non-trivial examples. Full Matlab implementations is also provided.