(a) Derive its frequency response. (b) Determine its response to the input x[n] = 10 + cos(n)+3 sin (n+ ). Hints: Use properties of LTI systems; 1+ ej0 = e (e-i + e%) = 2 cos()e; sin a = cos(a-5); 10 = 10 e 0m. Problem 4 Consider an LTI system whose frequency response H(w) is of the following type for some parameters a and b, 3 and that yields the following input-output pair.

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(a) Derive its frequency response.
(b) Determine its response to the input xn = 10+ cos
(n) +3 sin (n + ).
Hints: Use properties of LTI systems;
1+ e3® = ej% (e cos(a-5); 10 = 10 ež.0.n
+ e%) = 2 cos()e%; sin a =
cos(a-); 10 = 10 e.0.n
Problem 4
Hlwh
Consider an LTI system whose frequency response H ()
is of the following type for some parameters a and b,
and that yields the following input-output pair.
Ren] > y[n]
[n]
x[n]
in
-4-3-2-10 1234
3-2-1
1 2 3 4
Show that there is enough information to obtain the values of a and b. and give these values.
Hint: Express rn in the form ap eon +0 elwin with wo 0 and w= T.
Transcribed Image Text:Tools HW9-2.pdf HW9-2sol.pdf HW8-2.pdf 1/1 116% (a) Derive its frequency response. (b) Determine its response to the input xn = 10+ cos (n) +3 sin (n + ). Hints: Use properties of LTI systems; 1+ e3® = ej% (e cos(a-5); 10 = 10 ež.0.n + e%) = 2 cos()e%; sin a = cos(a-); 10 = 10 e.0.n Problem 4 Hlwh Consider an LTI system whose frequency response H () is of the following type for some parameters a and b, and that yields the following input-output pair. Ren] > y[n] [n] x[n] in -4-3-2-10 1234 3-2-1 1 2 3 4 Show that there is enough information to obtain the values of a and b. and give these values. Hint: Express rn in the form ap eon +0 elwin with wo 0 and w= T.
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