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1093:, one can prove that the signal energy is always equal to the summation across all frequency components of the signal's spectral energy density.
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1034:). Again, these units of measure are not dimensionally correct in the true sense of energy density as defined in physics. Dividing
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and the other sciences. The two concepts are, however, closely related, and it is possible to convert from one to the other:
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would represent the signal's spectral energy density (in volts·second per meter) as a function of frequency
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515:{\displaystyle E_{s}\ \ =\ \ \langle x(n),x(n)\rangle \ \ =\sum _{n=-\infty }^{\infty }{|x(n)|^{2}}}
298:{\displaystyle E_{s}\ \ =\ \ \langle x(t),x(t)\rangle \ \ =\int _{-\infty }^{\infty }{|x(t)|^{2}}dt}
163:) is defined as the area under the squared magnitude of the considered signal i.e., mathematically
831:{\displaystyle {\frac {\rm {{V}^{2}}}{\rm {\Omega }}}{\rm {{s}={\rm {{W}{\rm {{s}={\rm {J}}}}}}}}}
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represents the magnitude, in appropriate units of measure, of the load driven by the signal.
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Energy in this context is not, strictly speaking, the same as the conventional notion of
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645:{\displaystyle E={E_{s} \over Z}={1 \over Z}\int _{-\infty }^{\infty }{|x(t)|^{2}}dt}
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unit for energy as defined in the physical sciences.
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per meter) of an optical signal propagating through
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1139:"Power and Energy of a Signal : Demystified"
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109:Learn how and when to remove this message
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717:would appear as volt·seconds, which is
929:{\displaystyle \ E_{s}(f)=|X(f)|^{2}}
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47:adding citations to reliable sources
1081:units for spectral energy density.
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529:Relationship to energy in physics
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155:of a continuous-time signal
16:Concept in signal processing
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372:of a discrete-time signal
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1063:{\displaystyle E_{s}(f)}
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1108:Parseval's theorem
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99:December 2006
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60: –
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54:Find sources:
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32:This article
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1146:. Retrieved
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41:Please help
36:verification
33:
1148:2023-03-20
1124:References
980:free space
69:newspapers
947:) is the
783:Ω
672:potential
601:∞
596:∞
593:−
589:∫
477:∞
472:∞
469:−
459:∑
446:⟩
416:⟨
254:∞
249:∞
246:−
242:∫
229:⟩
199:⟨
1163:Category
1097:See also
342:And the
307:Unit of
539:physics
83:scholar
939:where
873:
844:, the
842:joules
654:where
535:energy
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127:energy
125:, the
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1032:hertz
976:volts
676:volts
90:JSTOR
76:books
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688:ohms
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