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Convert the analog filter with system function, Ha(s)=s+0.5(s+0.5)2+16

Convert the analog filter with system function,

Ha(s)=s+0.5(s+0.5)2+16

into a digital IIR filter using the bilinear transformation. The digital filter should have a resonant frequency of ωr=π/2.

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Solution:

From the system function, we observe that Ωc=4. The sampling period T can be determined using the equation,

Ωc=2Ttanωr2

T=LΩctanωr2=L4tanπ4=0.5 s

H(z)=H(s)|s=2T(1z11+z1)=H(s)|s=4(1z11+z1)

H(z)=s+0.5(s+0.5)2+16|s=4(1z11+z1)

=4(1z11+z1)+0.5[4(1z11+z1)+0.5]2+16=[4(1z1)+0.5(1+z1)][1+z1][4(1z1)+0.5(1+z1)]2+16[1+z1]2=4.5+z13.5z236.25+0.5z1+28.25z2

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