This paper is concerned with a problem of choosing optimum input test signals for estimating response functions or transfer functions of discrete-time systems. Under the amplitude constraint of signals and some additional appropriate assumptions it is shown that, in the case of identifying response functions, a pseudorandom binary sequence of input signals with as small correlations as possible is optimum in the sense that it maximizes a quantity of information provided by measurements. In the case of estimating unknown coefficients of transfer functions, an optimum scheme of step-by-step choice of input signals is proposed.