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Obtain digital filter transfer function by applying impulse in variance transfer function.
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ANS

H(s)=5(S+5)(S+2) if T=0.1s

Solution: Given:

H(s)=s(s+5)(s+2)

Step 1: Obtain h(t) By I.L.T.

By PFE.

H(s)=As+5+Bs+2

A=(s+5)H(s)|s=5 A=5/3

B=(S+2)H(S)|S=2 B=2/3

H(s)=513s+5213s+2

[h(t)=53e5tu(t)23e2tu(t)]

Step 2: Replace t = nT

h(n)=53e5nTu(n)23e2nTu(n)

Step 3: Apply Z.T.

H(z)=n=0h(n)˜zn=1n=053e5nTznn=023e2nTzn

=5311e5Tz12311e2Tz1

H(z)=5311e5Tz12311e2Tz1

T=0.1sec

H(z)=5/310.6065z12/310.8187z1

=16671.3645z10.667+0.4043ζ1(10.8187z10.6065E1+0.4965ζ2)

H(2)=10.9602z1114252z1+04965ζ2

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