On the approximation of analog systems with digital filters

The problem of approximation of an analog system by means of a digital filter, as it arises in typical echo cancellation problems, is considered. In a first case, the input signal of the analog system originates from the input signal of the digital filter via D/A conversion as is the case of echo cancellation in full duplex data transmission. In the second case, the input signal of the digital filter originates from the input signal of the analog system via A/D conversion, as is the case of echo cancellation in long-distance telephone circuits