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Obtain digital filter transfer function by applying impulse in variance transfer function.
1 Answer
written 5.6 years ago by | • modified 5.6 years ago |
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+5−213s+2
∴[h(t)=53e−5tu(t)−23e−2tu(t)]
Step 2: Replace t = nT
h(n)=53e−5nT⋅u(n)−23e2nTu(n)
Step 3: Apply Z.T.
H(z)=∑∞n=0h(n)˜zn=∑1n=053e−5nTz−n−∑∞n=023e−2nTz−n
=5311−e−5Tz−1−2311−e−2Tz−1
H(z)=5311−e−5Tz−1−2311−e−2Tz−1
T=0.1sec
H(z)=5/31−0.6065z−1−2/31−0.8187z−1
=1⋅667−1.3645z−1−0.667+0.4043ζ−1(1−0.8187z−1−0.6065E1+0.4965ζ−2)
H(2)=1−0.9602z−11−1⋅4252z−1+04965ζ−2