Analysis of Linear Systems by Means of Laguerre Functions

The use of Laguerre functions is proposed for the analysis of heavily damped linear systems where the input is not subject to experimental control. An equation is derived which links the corresponding coefficients in the Laguerre function expansions of the input, the impulse response and the output of a linear system. This equation enables the third set of Laguerre coefficients to be calculated when the other two sets of coefficients are known. The connection between the Laguerre function expansion and the representation of the system response by a series of gamma distributions is noted and the latter series identified as defining an analog system composed entirely of branches of linear storage elements.