IIR Butterworth Filter Design

[taolanino]

Hi, I used signal procesing tool box (FDA tool) to for my IIR FIlter design. I tried to obtain Differential Equation for this filter. This is what I have from Matlab. But I don't know how to apply these filter coefficients to get Differential Equation. Can you please help? Thanks

=======================
Section # 1
=======================
Numerator:
1
-2
1
Denominator:
1
0.94
0.45
Gain:
0.126

=====================
Section #2
=====================
Numerator
1
-1
0
Denominator:
1
0.37
0
Gain:
0.314
=====================
Output Gain:
1

 

[dxball]

MATLAB's FDA Tool is designed to split filters into 2nd order segments to maintain stability due to precision errors. Therefore, your difference equation is divided into two parts, where your first output is:

[latex] \[y_1[n] = gain_1 [\sum_{k=0}^{M_1}{b_1[k]x[n - k]} - \sum_{k = 0}^{N_1}{a_1[k]y_1[n-k]}] \] [/latex]

Then you would need to put that into your 2nd stage IIR filter where your output would be:

[latex] \[y[n] = gain_2 [\sum_{k=0}^{M_2}{b_2[k]y_1[n - k]} - \sum_{k = 0}^{N_2}{a_2[k]y[n-k]}] \] [/latex]

Sorry about not knowing how to use the tex formula editor in this site. But, hopefully you get the idea.