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A system is described by the following difference equation. Find out its transfer function H(z).

y[n]=34y[n1]18y[n2]+x[n]+12x[n1]

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 10

Year : DEC 2014

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By using z-transform,

Y(z)=34y(z)z118y(z)z2+x(z)+12x(z)z1Y(z)(134z1+18z2)=x(z)(1+12z1)y(z)x(z)=(1+12z1)(134z1+18z2)H(z)=z(z+12)(z234z+18)H(z)z=(z+12)(z12)(z14)

By partial fraction,

$\dfrac{H (z)}z= \dfrac A{(z-1⁄2)} …

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