Determining the Periodicity of the Sum of Periodic Signals

Determining the Periodicity of the Sum of Periodic Signals...

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Determining the periodicity of the sum of periodic signals Let x(t) = x 1 (t) + x 2 (t) + … x N (t) where x j (t) is a periodic signal with fundamental period T j seconds, j = 1,2…N. To determine whether x(t) is periodic , form the ratios T 1 / T j , j=2,…N. If every one of the ratios is a rational number, then x(t) is periodic. Otherwise, it is not periodic. If x(t) is periodic, we determine its fundamental period as below
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Unformatted text preview: : 1. Convert the ratios T 1 / T j , j = 2,N to a ratio of integers, with common factors between numerator and denominator canceled out. Now the ratios will be of the form N j / D j , for j=2,N. 2. Find the least common multiple (LCM) of the D j s. Let this number be K. 3. The fundamental period of x(t), T, is then given by T = K T 1 seconds...
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