For example, x(t)= cosw1t + cosw2t, determine the fundamental period and frequency of the signal.

T1 = 2$ \pi $/w1, T2=2$ \pi $/w2.

period T of x(t) must be s.t. T*w1 = N*2$ \pi $

or T*w2 = M*2$ \pi $ (both N and M are integers)

if T1/T2 is irrational, x(t) is non-periodic.

else if T1/T2 = N/M, s.t. M*T1 = N*T2

x(t) is periodic with fundamental period T = M*T1 = N*T2

and fundamental frequency w = 2$ \pi $/T

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Seraj Dosenbach