The article describes a new approach to solving of the problem of the statistical identification of the impulse response function with the auto- and cross-correlation functions of a linear dynamic system in a digital form. This approach is based on the use of the sign-function analog-stochastic quantization as a primary analog-to-digital conversion of the input and output of the considered system. The basis of the sign-function stochastic quantization is the use of the random auxiliary signals, which perform the function of a threshold stochastic quantization. Sign-function analog-stochastic quantization allows a coarse binary quantization without a bias and regardless of the statistical properties of the investigated random signals. The binary representation of the input and output signals of the system made possible an analytical calculation of the operators of integration in the development of the digital algorithms for estimation of the impulse response functions. The main result of the use of the sign-function analog-stochastic quantization is the transition from processing of multi-bit samples of the input and output signals to processing of the integer values of the time intervals defined by the change of the sign of the quantization result. This improves the data processing in the identification system. The final algorithms obtained for the calculation of the digital samples of the impulse response function does not require preliminary estimates of a direct calculation of the auto- and cross-correlation functions. They can be used for an online identification in real-time. A practical application of these algorithms improves the performance of the digital statistical processing of the input and output signals of the system. A brief account of the algorithmic diagram is presented. It shows the sequence of the basic instructions to be performed for calculation of the samples of the impulse response function