_Signal_FAQ08_Finite_Power_Signal

_Signal_FAQ08_Finite_Power_Signal - What is the energy and...

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What is the energy and power spectra for a finite power signal? How do we know if a signal is of finite power? Let ( 29 t x 1 be a finite energy signal with a spectrum of ( 29 ( 29 [ ] t x f X 1 1 F = . The power of the signal is the mean square value ( 29 ( 29 = = - 2 2 2 1 2 1 1 1 Lim T T T dt t x T t x p , and the energy is ( 29 - = 2 2 2 1 1 Lim T T T dt t x e . In the frequency domain, these can also be obtained by using ( 29 ( 29 - - = = df f X df f E e 2 1 1 1 and ( 29 ( 29 - - = = df T f E df f P p T 1 1 1 Lim , where ( 29 ( 29 2 1 1 f X f E = = Energy spectrum and ( 29 ( 29 T f E f P T 1 1 Lim = = Power spectrum. Since the signal is of finite power, ( 29 - = df f P p 1 1 = Finite and
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( 29 ( 29 = = T f E f P T 1 1 Lim Finite. However, the energy and energy spectral density will approach infinity: ( 29 ( 29 [ ] = f TP
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This note was uploaded on 08/02/2009 for the course ECE EE2009 taught by Professor Prof.c.c.ko during the Fall '07 term at National University of Singapore.

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_Signal_FAQ08_Finite_Power_Signal - What is the energy and...

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