Band-pass and equivalent low-pass signal modeling
Band-pass and equivalent low-pass signal modeling
Band-pass and equivalent low-pass signal modeling
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<strong>B<strong>and</strong></strong><strong>pass</strong> r<strong>and</strong>om <strong>signal</strong>s <strong>and</strong> noise (3)<strong>and</strong> henceRRxxy( τ ) = R ( τ )y( τ) =−R( τ)R ~ ( τ ) = 2R( τ ) + 2 jR ( τ )nxyxxy(29)(30)Note that the autocorrelation of the complex envelope may be complex (but thespectrum is real!)Fourier transforming (27) we get1S ( f) = [ S~ ( f − f ) + S~( −f − f )]n 4 n c n c(31)As before we find <strong>low</strong>-<strong>pass</strong> spectrum(U(f) is the "unilateral step function")© NOKIA FILENAME.PPT / 13.12.1997 / NN page: 21
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