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lecture15

# lecture15 - Lecture Outline(Week 8 lecture 1 More on Signal...

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Lecture Outline (Week 8, lecture 1) More on Signal Space Representations Carier-Amplitude Modulation - Basics Reading: Finish reading entire chapter 5 of text1. May start early part of chapter 7. 1. Geometric Representation of signal waveforms. Signal ) ( t s i expressed by coordinates for a set of orthonormal functions N n n t 1 )} ( { = ψ , i.e. 1 ) ( ) ( 0 = T n m dt t t ψ ψ if n m = and 0 ) ( ) ( 0 = T n m dt t t ψ ψ if n m The coordinates are given by = T n i n i dt t t s s 0 , ) ( ) ( ψ Each signal can now be represented by a point with these coordinates for N n 1 . The distance between 2 signal points is given by 2 , , 2 2 ) ( | | n j n i j i ij s s s s d - = - = Noise for the coordinates are independent and identical distributed (i.i.d.) Gaussian random variable with variance 2 / 0 N . Demodulation is found by correlation of received signal ) ( t r with the basis functions. ) ( t r represented by vector r with coordinates = T n n dt t t r r 0 ) ( ) ( ψ for N n 1

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