extra 8 - impulse functions to represent these values....

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1 Power and Energy For a voltage function f ( t ), its power is | f ( t )| 2 and its energy is | f ( t )| 2 dt . assuming loading resistance R =1. There is a clear difference between the two. Following this, we will sometimes say that | f ( t )| 2 and | f ( t )| 2 dt are the power and energy of f ( t ), respectively. We will not specify the resistance value R. In other words, we assume default value R =1. When f ( n ) is a sampled value, we still say that | f ( n )| 2 is the power of f ( n ). However, sometimes we may also say that | f ( n )| 2 is the energy of f ( n ). Note that there is no confusion here, since | f ( t )| 2 dt is not defined in this case. In other words, for a sampled system, we may regard power and energy as the same. t f ( t ) n f ( n )
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2 Line Spectrum For a periodic signal with period T , its power spectrum is distributed over discrete points 2 π k / T , k =0, ± 1, ± 2, … Mathematically, we should use
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Unformatted text preview: impulse functions to represent these values. However, for convenience, we may simply use the so-called line spectrum as shown below. We sometimes also assume that the signal is real and use only the positive half after adding the negative half of the spectrum to the positive half, which is purely for convenience. It will not cause confusion as the related power spectrum is symmetric. For example, the follow are the one-sided and two-sided line spectrums for cos(2 f c t ). (Note that the average power of cos(2 f c t ) is 0.5.) Please treat these as engineering convenience. In old days, without computer, drawing a plot is quite time-consuming. We want to save effort and use some notations that mathematicians may not like. -f c f f c 0.5 f f c 0.25...
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This note was uploaded on 01/11/2011 for the course EE 3008 taught by Professor Pingli during the Fall '08 term at City University of Hong Kong.

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extra 8 - impulse functions to represent these values....

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