Sine-cosine wavelets, shifted Legendre polynomials, Chebyshev wavelets, Legendre wavelets and their operational matrices of integration are successfully applied for the analysis of observer design in the singular system of transistor circuits. The idea is that the states and the plant inputs are expressed in terms of these orthogonal functions. The method simplifies the system of state equations into the solution of a set of linear algebraic equations. Further, the algorithms can be easily implemented in a digital computer and the solutions can be obtained for any length of time. It seems, even with a relatively low number of terms, most of the proposed algorithms give more accurate results when compared with the other possible approximations. The given example supports this claim.