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A digital filter with a 3 dB bandwidth of 0.4 is to be designed from the analog filter whose system response is, H(s)=Ωcs+2Qc...

A digital filter with a 3 dB bandwidth of 0.4 is to be designed from the analog filter whose system response is:

H(s)=Ωcs+2Ωc

Use the bilinear transformation and obtain H(z).

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Solution:

We know that,

Ωc=2Ttanωc2

Ωc=2Ttan0.4π2=1.453T

This system response of the digital filter is given by,

H(z)=Ha(s)∣=2T(1z11+z1)

=Ωc2T(1z11+z1)+2Ωc=1.453T2T(1z11+z1)+2(1.453T)

=1.453(1+z1)2(1z1)+2(1+z1)1.453=1+z13.3760.624z1

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