Simplified method of determining transient response from frequency response of linear networks and systems

Knowing the frequency response of a linear system, a method is presented for obtaining the time response of the system to an impulse, step, or ramp function input, without performing graphical integrations. The transient response is of the formf(t) = \sum\min{i} A_{i}G(\omega_{i}t)where a different functionGis used to determine the response to each of the three types of input. Tables of the functionsG(x)are provided. An example is given to illustrate the simplicity and accuracy of this method. The results are compared with the exact time response.