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Using the bilinear transformation, obtain H(z) from Ha(s) when T = 1s and Ha(s)=s3(s+1)(s2+2s+2)
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Solution:

Given this equation,

Ha(s)=s3(s+1)(s2+2s+2) and T=1 s

To obtain H(z) using the bilinear transformation, put s=2T(1z11+z1) in Ha(s).

H(z)=Ha(s)|s2T(1z11+z1)=s3(s+1)(s2+2s+2)|s=2(1z11+z1)

=[2(1z1)(1+z1)]3[2(1z1)1+z1+1]{[2(1z1)1+z1]2+2[2(1z1)1+z1]+2}=8(1z1)3[2(1z1)+(1+z1)][4(1z1)2+4(1z1)(1+z1)+2(1+z1)2]

=8(1z1)3(3z1)[104z1+2z2]=4(1z1)3(3z1)(52z1+2z2)=4(13z1+3z2z3)1511z1+8z22z3

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