The Colored Noise Gain Function of the Single Input and Single Output Discrete-time System

A method for obtaining the colored noise gain function is proposed. The colored noise gain function is the function which gives the auto-covariance of the output signal of SISO (single input and single output system) from the auto-covariance of the input singnal. The input signal is asumed to be white or colored Gausian noise. And ACF(auto-covariance function) for ARMA (autoregressive moving average) model is derived from the proposed function with white noise input in closed form. Some results of the calculation of ACF with white noise input and the simulation of the system with colored noise input show the effectiveness of the proposed method.