Ve451Su2010C4

# Ve451Su2010C4 - Ve451 Lecture Notes Dianguang Ma Summer...

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Unformatted text preview: Ve451 Lecture Notes Dianguang Ma Summer 2010 Chapter 4 Frequency Analysis of Signals Frequency Analysis of Continuous-Time Periodic Signals 2 2 2 2 Let ( ) be a periodic signal with fundamental period 1/ , we have ( ) (synthesis equation) 1 ( ) (analysis equation) 1 ( ) (average power) p p p j kF t k k j kF t k T p x k T k p x t T F x t c e c x t e dt T P x t dt c T π π ∞ =-∞- =-∞ = = = = = ∑ ∫ ∫ ∞ ∑ Frequency Analysis of Continuous-Time Aperiodic Signals 2 2 Let ( ) be an aperiodic signal, we have 1 ( ) ( ) ( ) 2 (synthesis equation / inverse transform) ( ) ( ) ( ) (analysis equation / direct transform) j Ft j t j Ft j t x x t x t X F e dF X e d X F x t e dt x t e dt E x π π π ∞ ∞ Ω-∞-∞ ∞ ∞-- Ω-∞-∞ = = Ω Ω = = = ∫ ∫ ∫ ∫ 2 2 2 1 ( ) ( ) ( ) 2 (total energy) t dt X F dF X d π ∞ ∞ ∞-∞-∞-∞ = = Ω Ω ∫ ∫ ∫ Frequency Analysis of Discrete-Time Periodic Signals 1 2 / 1 2 2 / 1 2 Let ( ) be a periodic signal with fundamental period...
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Ve451Su2010C4 - Ve451 Lecture Notes Dianguang Ma Summer...

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