What is the impulse response of the system described by the second order difference equation y(n)-3y(n-1)-4y(n-2)=x(n) 2x(n-1)? - Study24x7
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Goraksha Dadhich
30 Mar 2019 11:06 AM study24x7 study24x7

What is the impulse response of the system described by the second order difference equation y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1)?

A

[-1/5 (-1)n-6/5 (4)n]u(n)

B

[1/5 (-1)n – 6/5 (4)n]u(n)

C

[ 1/5 (-1)n+ 6/5 (4)n]u(n)

D

[- 1/5 (-1)n+ 6/5 (4)n]u(n)

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  • geet sharma
    •  The homogenous solution of the given equation is yh(n)=C1(-1)n+C2(4)n—-(1)
    To find the impulse response, x(n)=δ(n)
    now, for n=0 and n=1 we get
    y(0)=1 and
    y(1)=3+2=5
    From equation (1) we get
    y(0)=C1+C2 and
    y(1)=-C1+4C2
    On solving the above two set of equations we get
    C1=- 1/5 and C2= 6/5
    =>h(n)= [-1/5 (-1)n + 6/5 (4)n]u(n).

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    Reply 30 Mar 2019 11:41 AM
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