Fourier Analysis for Continuous Time Processes

Abstract

Any periodic function with a frequency f ₀ , i.e., period T ₀= 1/f ₀, not only repeats itself with period T ₀ , but also in periods of 2T ₀, 3T ₀ , 4T ₀, etc. Therefore, a set of periodic functions with frequencies F _p , 2F _p ,3F _p , 4F _p ,…kF _p when combined (added) will be periodic with period T _p =1/F _p (which is the lowest common period). In other words periodic functions display the property that when a periodic function with a certain frequency (called fundamental frequency) is added to one or more of its harmonics (functions with frequencies that are multiples of the fundamental frequency) a new periodic function with exactly the same period as the fundamental is obtained.