Question

sin((n-16)/4) (n-16) Consider an LTI discrete-time system that has impulse respo 6)/4) if n #16 if otherwise a) Determine the magnitude H(12) and the phase response ZH(12) for –< 1 < . Enter 12 as “O” and enter the piecewise function |H(12) using the heaviside function. |H(12) = ZH(12) = b) Determine the output of the system, y[n], if the input is given by x[n] = S[n – 9] + cos( 72 ). Enter your answer in terms of h[n]. y[n] = In your answers, enter z(n) for a discrete-time function z[n]. WebWork is unable to parse a function that uses square brackets.

Answer 1

@ hen I sin carcn-16) m+ 6 T(n-16) else We have sin an erect ( 17 ) for <KT sin ( cafe at the end th . We have shifting property if Ich) 8 x(n-no) x V) e uno (2) G

sin (11 (M-16)) .js 16 761-16) G ērn vect.com : HM= reet ( 4 ) eliber 1H (W)) = /pect (1 772) I Leon 1+ lopp! & H()) = rect (m 2 ) JARDI - (-orn - (4+0) n * = (adu!

uffet uk)= C or else" SIA u 6 - 1) = { } NI I o eles |HCC)) = 4 (-1* £)- un phase (H) = Lelion - 160 210) S(-9) cos ( n). We have yin)= an *hin) we have Sm*sin-ng) = SM-no) Sm-9) * hin) = h (n=9)=y, (n) Ye (n) = cos (1/ h) * hin) iz ()= H (32) ascun + ZH ()) where 14 (7)]=1

n (mat) 50 + (-wy cuki (uge soy =(U12h treuisſujuist (17)50 (um) so s (uz-ui) soy =(w3cm 1:32 + x - (+7 17- = JlX91-