Implementing IIR/FIR Filters
Implementing IIR/FIR Filters
Implementing IIR/FIR Filters
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Network Diagram<br />
x(n)<br />
Transfer Function<br />
Gain<br />
Phase<br />
Coefficients<br />
z -1<br />
z -1<br />
G( θ)<br />
α<br />
2α<br />
α<br />
Hz ( )<br />
Σ<br />
Figure 2-10 Direct-Form Implementation of Second-Order Lowpass <strong>IIR</strong> Filter and<br />
Analytical Formulas Relating Desired Response to Filter Coefficients<br />
MOTOROLA 2-13<br />
2<br />
γ<br />
−β<br />
α 1 2z 1 –<br />
z 2 –<br />
( + + )<br />
1/2 γz 1 –<br />
– βz 2 –<br />
= --------------------------------------------<br />
+<br />
z -1<br />
z -1<br />
( 1 + cosθ)<br />
( 1 – cosθc)<br />
( dsinθsinθc) 2 4( cosθ<br />
– cosθc)<br />
2<br />
[ +<br />
] 1/2<br />
= --------------------------------------------------------------------------------------------------<br />
φθ ( )<br />
tan 1 – 2 θ θ ( cos – cos c)<br />
--------------------------------------dsinθsinθc<br />
– π tan 1 – 2 θ θ ⎧<br />
⎪<br />
⎪<br />
= ⎨<br />
⎪<br />
( cos – cos c)<br />
⎪ + ----------------------------------------<br />
⎩<br />
dsinθsinθc 1<br />
β ⎛--⎞ 1 d 2<br />
⎝2⎠ ⁄ θ – sin c<br />
= ---------------------------------<br />
1+ d ⁄ 2sinθc<br />
γ = ( 1/2 + β)<br />
cosθc<br />
α =<br />
( 1/2 + β– γ)/4<br />
y(n)<br />
for θ≤θ c<br />
for θ>θ c
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