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 />
−α<br />
Hz ( )<br />
α 1 z 2 –<br />
( – )<br />
1/2 γz 1 –<br />
– βz 2 –<br />
= --------------------------------------------<br />
+<br />
dsinθosinθ ( dsinθsinθ0) 2 4( cosθ<br />
– cosθ0)<br />
2<br />
[ +<br />
] 1/2<br />
= --------------------------------------------------------------------------------------------------<br />
– 1<br />
φθ ( ) – tan<br />
2 θ θ ( cos – cos 0)<br />
= ---------------------------------------dsinθsinθ0<br />
d<br />
Σ<br />
2tan ( θ0 /2Q)<br />
= ----------------------------------sinθ0<br />
1<br />
β ⎛--⎞ ⎝2⎠ 1 tan θ0 /2Q ( )<br />
–<br />
= -------------------------------------<br />
1+ tan( θ0 /2Q)<br />
γ = ( 1/2 + β)<br />
cosθ0<br />
α = ( 1/2 – β)/2<br />
Figure 2-19 Direct-Form Implementation of Second-Order Bandpass <strong>IIR</strong> Filter and<br />
Analytical Formulas Relating Desired Response to Filter Coefficients<br />
2-24 MOTOROLA<br />
2<br />
γ<br />
−β<br />
z -1<br />
z -1<br />
y(n)