AbstractAssume that signal f(t) is impressed on N parallel time‐invariant linear networks Hm(w)(m=1∼N), and consider the uniformly sampled values gm(nT)(m = 1∼N; n = 0, ±1, ±2,; T <0) of the output signal gm(t)(m=l∼N). This paper discusses the following problem from a unified viewpoint. The response g(t), when the signal f(t) is passed through the given filter H(w), is to be approximated by an expression y(t) which is the sum of the forementioned sample values multiplied by time functions ψmn(l)(m = 1∼N; n= 0, ±1, ±2, ). It is assumed that the signal f(t) belongs to the set l of the signals for which the weighted square integral of the Fourier spectrum F(w) is not greater than a positive number A. In the foregoing, ψmn(t) is called the interpolation function.First, it is shown that given Hm(w)(m =1∼N), the time‐limited interpolation function, which minimizes the upper limit emax(t) of the error e(t) = [g{t)‐y(l)] over all f(t) belonging to F, is obtained by shifting the impulse responses ψ(l)(m=1∼N) of certain N linear time‐invariant interpolation filters ψ()w(m=1∼N) along the time axis. The analytic form for this function is given. Assuming that Hm(w) (m=1∼N and ψm(w)(m=1∼N) are optimized so that the measure emax(t) of the error is minimized, the upper and the lower bounds of the optimal emax(t) are shown. Considering an application where N is large, the optimization is discussed in the sense that the equivalent multiplicity is reduced at the sacrifice of the approximation error.