Note on the approximation problem

NETWORK synthesis is the aggregate of concepts and procedures utilized in obtaining an electric network whose performance approximates an arbitrarily prescribed performance. The performance specified may be the desired time response to a given excitation, such as a step or impulse function. More usually, it is the magnitude of the steady-state transfer function over all or part of the frequency axis; or it may be the angle of this function specified over all or part of the frequency axis, or it may be some combination of these over parts of the frequency axis. This paper is concerned only with a magnitude function prescribed over part or all of the frequency axis. The network functions of interest are output over input functions, with any combination of voltage or current as output and input. All of these are functions having similar properties. To include them all in the discussion the transfer function F will be defined as a function specifying the output of a network divided by the input.