extra 4 - Power Spectrum |S(f)|2 energy spectrum f -2/τ...

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Unformatted text preview: Power Spectrum |S(f)|2 energy spectrum f -2/τ -1/τ 1/τ 2/τ |P(f)|2 power spectrum Definition: -2/τ -1/τ 1/τ 2/τ f power spectrum = energy spectrum /T In the above, T is the time span of a signal. For example, for a signal contains 12 pulses as shown below, then T=12τ. Note that this definition is somewhat ambiguous as the zero part can also be counted in the signal. However, no matter how to choose T, the shape of the power spectrum is the same. Sometimes we will call it “normalized power spectrum” since T is just a normalization constant. τ 1 Average Power Spectrum . . . If we consider all the possibilities of the signs in a pulse string, the “average power spectrum” is the average of the power spectrums of all possible signals. It can be proved that the “average power spectrum” has the same shape as energy spectrum of a single pulse. (See tutorial 2 Q2.) |P(f)|2 power spectrum -2/τ -1/τ 1/τ 2/τ f 2 Integrator Receiver s(t) 0 τ bs(t) t ⊗ bs2(t) ∫0 τ τ y digital signal z decision device reference signal s(t) PDF for b=1 -Aτ 0 Aτ y =Aτ+η PDF for b=-1 -Aτ 0 Aτ y = -Aτ+η 3 ...
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extra 4 - Power Spectrum |S(f)|2 energy spectrum f -2/τ...

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