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### IIR filter example

IIR filter short form is for infinite impulse response. In IIR filter design that are following criteria should be satisfied by designing the digital filter in the analog domain and transforming into a digital domain.

The transfer function of analog filter is :

H(s) = 3 / (s+2) (s+3) with Ts = 0.1 sec

Design the digital IIR filter using BLT.

H(s) = 3 / (s+2) (s+3)........................(1)

In BLT H(Z) is obtained by putting :

s = 2/Ts [ Z-1/Z+1] here Ts = 0.1 sec

s = 2/0.1 [ Z-1/Z+1]

s = 20 [ Z-1/Z+1]

Putting this value in equation (1) we get,

H(Z) = 3 / [ 20*(Z-1/Z+1)+2] [  20*(Z-1/Z+1)+3]

H(Z) = 3 / [(20Z-20/Z+1) + 2] [ (20Z-20/Z+1 ) + 3 ]

H(Z) = 3 (Z+1) (Z+1) / (20Z-20+2Z+2) (20Z-20+3Z+3)

H(Z) = 3 (Z+1)/  506Z2-374Z-414Z+306
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H(Z) = 3  (Z2+ 2Z +1 )/  506Z2-788Z+306

H(Z) =  (Z2+ 2Z +1 )/  168.67Z2-262.67Z+102

This function required a function for digital IIR filter
IIR filter short form is for infinite impulse response. In IIR filter design that are following criteria should be satisfied by designing the digital filter in the analog domain and transforming into a digital domain.

The transfer function of analog filter is :

H(s) = 3 / (s+2) (s+3) with Ts = 0.1 sec

Design the digital IIR filter using BLT.

H(s) = 3 / (s+2) (s+3)........................(1)

In BLT H(Z) is obtained by putting :

s = 2/Ts [ Z-1/Z+1] here Ts = 0.1 sec

s = 2/0.1 [ Z-1/Z+1]

s = 20 [ Z-1/Z+1]

Putting this value in equation (1) we get,

H(Z) = 3 / [ 20*(Z-1/Z+1)+2] [  20*(Z-1/Z+1)+3]

H(Z) = 3 / [(20Z-20/Z+1) + 2] [ (20Z-20/Z+1 ) + 3 ]

H(Z) = 3 (Z+1) (Z+1) / (20Z-20+2Z+2) (20Z-20+3Z+3)

H(Z) = 3 (Z+1)/  506Z2-374Z-414Z+306
-
H(Z) = 3  (Z2+ 2Z +1 )/  506Z2-788Z+306

H(Z) =  (Z2+ 2Z +1 )/  168.67Z2-262.67Z+102

This function required a function for digital IIR filter