In the article, we study the simulation of the input signal, which is applied to a linear system with known impulse response function. System response is an output process. With the help of the Karhunen–Loeve expansion, a model is constructed which approximates the input process taking into account the output with predefined accuracy and reliability in the Banach space C([0, T ]). Also, a partial case is investigated, in which the input process is the Brownian motion.
