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DC Component of Power Spectrum of Random Binary Bits toggling from +1 and -1 ?

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JohnLai

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Hi,

I am reading Behzad Razavi's "Design of Integrated Circuits for Optical Communication". In Eq. (2.2), it describes the power spectrum of a random binary bit sequence as,

Sx(f) = (1/Tb) * |P(f)|^2,

where x(t) = Σ bk * p(t-k*Tb) for bk = ±1 and P(f) = Tb*sinc(f*Tb)

Since x(t) toggles between +1 and -1 with equal probability. The DC component should be zero. But from the above equation, P(f) is a sinc function and contains non-zero value at DC.

Do you know know how to explain this discrepancy.

Thanks.
 

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