quiz11_08 - ¸ j a 2 j ² je j n ² je ² j n b 2 ² je j...

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ECEN 487 QUIZ 11 NAME:____KEY______ 1.(10) What is the frequency causal analytic signal, x a [ n ], which corresponds to the real signal x [ n ] = a sin ± 0 n + b co s ± 1 n , ± o ± ± 1 ? Draw a block diagram to show how x a [ n ] can be generated from x [ n ]. x i [ n ] is just a 90 ° phase delay of x r [ n ] , so x a [ n ] = x r [ n ] + jx i [ n ] = a s in ± 0 n + b co s ± 1 n + j (- a cos ± 0 n + b sin ± 1 n ) or: x [ n ] = a 2 j e j ± 0 n ² e ² j ± 0 n ( ) + b 2 e j ± 1 n + e ² j ± 1 n ( ) x a [ n ] = a 2 j e j ± 0 n ² e ² j ± 0 n ( ) +
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Unformatted text preview: · ¸ + j a 2 j ² je j n ² je ² j n ( ) + b 2 ² je j 1 n + je ² j 1 n ( ) ³ ´ µ ¶ · ¸ = a j e j n + be j 1 n-j times positive frequency, j times negatiave frequency terms. Hilbert Transform x a [ n ] x [ n ] x r [ n ] x i [ n ]...
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