Unformatted text preview: 1 [·], and the second subsystem is the one we have been
considering. xc[n] h1[.] h[.] yc[n] Figure 4: Composite system. 10. [4 points]: What is the output yc [·] of the composite system? It is essential that you explain
your reasoning here. Page 9 of 17 6.02 Fall 2012, Quiz 2 III Frequently We stick with the LTI system introduced in the previous section, namely the system with unit sample re
sponse h[n] = δ [n] − δ [n − 1] + δ [n − 2] .
11. [3 points]: Write down an explicit expression for the frequency response
H (Ω) = ∞
0 h[m]e−j Ωm m=−∞ of the particular LTI system speciﬁed above. H (Ω) = 12. [6 points]: Rewrite your answer from the previous part in the form
H (Ω) = A(Ω)ej α(Ω) ,
where α(Ω) and A(Ω) are real functions of Ω. [We don’t insist that A(Ω) be nonnegative, so A(Ω)
need not be the magnitude of H (Ω).] A(Ω) = , α(Ω) = Page 10 of 17 6.02 Fall 2012, Quiz 2
13. [4 points]: Evaluate A(Ω) and α(Ω) explicitly for Ω = A( π ) = 3 , , and for Ω = 2π
3 . α( π )...
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