_Signal_FAQ07_Finite_Energy_Signal

_Signal_FAQ07_Finite_Energy_Signal - What is the energy and...

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What is the energy and power spectra for a finite energy signal? How do we know if a signal is of finite energy? 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 energy, ( 29 ( 29 ( 29 = = = = - - - df f X df f E dt t x e T T T 2 1 1 2 2 2 1 1 Lim Finite and ( 29 ( 29 2 1 1 f X f E = =Finite.
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_Signal_FAQ07_Finite_Energy_Signal - What is the energy and...

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