What is the particular solution of the first order difference equation y(n) ay(n-1)=x(n) where |a| - Study24x7
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Goraksha Dadhich
30 Mar 2019 11:03 AM study24x7 study24x7

What is the particular solution of the first order difference equation y(n)+ay(n-1)=x(n) where |a|<1, when the input of the system x(n)=u(n)?

A

1/(1+a) u(n)

B

1/(1-a) u(n)

C

1/(1+a)

D

1/(1-a)

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  • geet sharma
    • The assumed solution of the difference equation to the forcing equation x(n), called the particular solution of the difference equation is
    yp(n)=Kx(n)=Ku(n) (where K is a scale factor)
    Substitute the above equation in the given equation
    =>Ku(n)+aKu(n-1)=u(n)
    To determine K we must evaluate the above equation for any n>=1, so that no term vanishes.
    => K+aK=1
    =>K=1/(1+a)
    Therefore the particular solution is yp(n)= 1/(1+a) u(n).

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    Reply 30 Mar 2019 11:46 AM
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