Abstract
The method of measuring a circuit's transfer function described here is based upon a test which employs an impulse function called the delta function. Since the delta function, which is a zero width spike of unit energy content, has frequency components of constant amplitude at all frequencies, the circuit output response is uniquely determined by the circuit transfer function.
In practice, although a true impulse can not be generated physically, a rectangular pulse with a very narrow pulse width (much less than the significant time constant of the system) usually provides a suitable approximation. The rectangular pulse function is a simple and convenient prototype for the impulse function but it is a discontinuous function. In certain problems of interest, it is desirable to use a prototype which possesses derivatives. Further, it is desirable to define the impulse function to be an even function of its argument. One such function is the gaussian pulse function. The gaussian pulse function hence satisfies the defining equation of the unit impulse function in the limit when σ, the standard deviation, approaches zero. Furthermore, the method for approximating the impulse response by the gaussian impulse can be easily extended to the random process by means of the auto- and cross-correlation functions of the process input and output signals.
The present paper is divided into two main parts. The first part is devoted to the development of a method of generating gaussian signal by an analog computer. The second part is concerned with the method to measure the parameter of the transfer function derived from the moment of the output response of the gaussian signal. It has become clear from the experimental results that this method is effective in finding the dynamic characteristics of adaptive control systems, because the transfer function can be estimated by the simple operation with sufficient accuracy.
