Tao Analysis/Tao Synthesis

A system is completely characterized when you know the relation, or function, or operator OUT/IN for each value of a variable of interest, such as the value of IN, the time or its inverse, frequency.
In some areas (Networks Theory) OUT / IN is called the Transfer Function of the system.

The procedure of Analysis of the system can be carried out when system is completely know, that is all its elements, their characteristics and functionalities, and all the relationships between the elements, the circuit, and one wants to establish the OUT/IN relationship. This, with previous assumptions, is always possible, even if only with numerical methods for very complicated systems.

The inverse procedure of Analysis is the Synthesis of the system, i.e. given a OUT/IN determine the system that creates it. This is not always possible, if not with methods and numerical approximations, even for OUT/IN relationship is relatively simple.

The two inverse procedures of Analysis/Synthesis therefore have a very different behavior. The situation is similar to that which occurs, for example, in Differential Calculus, where is relatively simple differentiable and integrable functions easily allow the calculation of the derivative function, but not, formally, the integral, except by numerical methods.