Input convertors for generators of symmetric functions

An analogue function generator for the production of a function f(x1, x2, ¿ xn) of the variables x1, x2, ¿, xn produces an output signal representing f for the instantaneous values of input signals that correspond to the variables. If f is a symmetric function, having, for example, simple or multiple symmetry of reflection, it is possible to transform the input variables into a new set which is restricted to a suitable region of the n-space of the variables. This can be done in an input convertor. The input variables having been transformed, a simpler function generator can be used for the production of f i.e. one whose operation is restricted to a region of n-space. It turns out that in many important cases the combination of convertor and simpler function generator is simpler than the generator which would be required for the direct production of the function. In many important instances convertors can consist of diode selection circuits in combination with linear circuits. They can be connected in cascade in order to take care of multiple symmetry and lead to interesting configurations. The Synthesis of convertor circuits follows at once from a suitable mathematical formulation of their operation.