A time-variable transform and its application to spectral analysis

THE USE OF integral transforms to solve dynamical problems in physics and engineering has received considerable prominence in the last half century. Integral transforms have, since their usefulness was discovered by Heaviside in the late nineteenth century, gone through the cycle of: (1) rigorization of technique;1, 2 (2) tabulation of many specific transform pairs;3, 4 and (3) generalization of transform methods.5–8. In the present paper on extension of this generalization will be made which is applicable only to time series and its use precludes the acceptance of the fundamental postulate of cause and effect. That is, the present response anywhere in a physical system can in no way depend on future values of a stimulus elsewhere in the system.