On the relation of circuit theory and signals, systems and communications

In signal processing, system theory, and in information theory signals are either complex valued waveforms or sequences of dimensionless complex numbers. The "power" of such signals is usually said to be the squared magnitude of these complex numbers. In an electrical circuit, power is always the product of voltage and current, both present at a port, i.e., at a pair of terminals. Here we ask the question: what is the relation between signal power and physical power? There are special cases, where the two notions of power are strictly proportional and, therefore, no conflict occurs. But in general, especially when we deal with vector signals, the commonly used squared Euclidean norm of the signal vector may not be a measure for the physical power associated with the voltages and currents, which correspond to the signal vector. In addition to the physically consistent computation of signal power, physically consistent modeling of the noise is crucial in all information processing systems. Again circuit theory provides a methodology to model how the noise comes into the system. Modeling is one of the most important tasks in engineering and, therefore, physically consistent modeling is very important for the education of electrical engineers. Circuit theory is the essential framework to ensure physical consistency across several levels of abstraction.