(New page: == Periodic and Non-Periodic Functions == '''Periodic''' In CT the cosine function cos(t) is a periodic function with fundamental period T = 2π. This comes from the definition of perio...) |
|||
| Line 1: | Line 1: | ||
| − | |||
== Periodic and Non-Periodic Functions == | == Periodic and Non-Periodic Functions == | ||
'''Periodic''' | '''Periodic''' | ||
| + | |||
In CT the cosine function cos(t) is a periodic function with fundamental period T = 2π. This comes from the definition of periodic systems. A function x(t) is periodic if there exists some T > 0 for which x(t + T) = x(t). In our case x(t) = cos(t) and T = 2π * n where n is an integer. | In CT the cosine function cos(t) is a periodic function with fundamental period T = 2π. This comes from the definition of periodic systems. A function x(t) is periodic if there exists some T > 0 for which x(t + T) = x(t). In our case x(t) = cos(t) and T = 2π * n where n is an integer. | ||
| + | |||
'''Non-Periodic''' | '''Non-Periodic''' | ||
| + | |||
In CT let x(t)=e^[1+j2)t]=(e^t)×[cos(2t)+ jsin(2t)] is a non-periodic signal because there is no T for which x(t+T)= x(t). In this case the signals amplitude goes to ∞ as t goes to ∞. | In CT let x(t)=e^[1+j2)t]=(e^t)×[cos(2t)+ jsin(2t)] is a non-periodic signal because there is no T for which x(t+T)= x(t). In this case the signals amplitude goes to ∞ as t goes to ∞. | ||
Latest revision as of 09:23, 5 September 2008
Periodic and Non-Periodic Functions
Periodic
In CT the cosine function cos(t) is a periodic function with fundamental period T = 2π. This comes from the definition of periodic systems. A function x(t) is periodic if there exists some T > 0 for which x(t + T) = x(t). In our case x(t) = cos(t) and T = 2π * n where n is an integer.
Non-Periodic
In CT let x(t)=e^[1+j2)t]=(e^t)×[cos(2t)+ jsin(2t)] is a non-periodic signal because there is no T for which x(t+T)= x(t). In this case the signals amplitude goes to ∞ as t goes to ∞.
