The problem of synthesizing nonlinear electronic systems executing the mapping a(cos t) yields y**0(t, a), where y**0(t, a) equals f(a) cos lt or y**0(t, a) equals gamma (t), is considered. This includes the synthesis of rectifiers, various amplitude detectors, frequency multipliers, and a number of other devices. The input signal a(cos t) is split and the problem then reduced to approximation (on the basis of the splitting obtained) of the output y**0(t, a). The proposal is made to perform the approximation using a rational function. It is shown that the two-dimensional problem of Chebyshev approximation that arises in this case reduces to a one-dimensional problem.