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For example, x(t）= cosw1t + cosw2t, determine the fundamental period and frequency of the signal. | For example, x(t）= cosw1t + cosw2t, determine the fundamental period and frequency of the signal. | ||
| − | T1 = 2<math>\pi</math>/w1, T2=2<math>\pi</math>/w2 | + | T1 = 2<math>\pi</math>/w1, T2=2<math>\pi</math>/w2. |
| + | |||
| + | period T of x(t) must be s.t. T*w1 = N*2<math>\pi</math> | ||
| + | or T*w2 = M*2<math>\pi</math> (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<math>\pi</math>/T | ||
Revision as of 16:07, 22 July 2009
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
