Combine fractions to have final digital filter transfer func

Assignment Help Electrical Engineering

Reference no: EM13264961

Consider the analog filter H(s)=30000/(s^2+400s+30000) , notice that the filter gain in the passband is unity or 0 dB. You can also use MATLAB command "roots" to check for the poles that are p_1=-100 rad/s, and p_2=-300 rad/s.

Use MATLAB commands "bode" and "impulse" to obtain the graphs of the filter frequency response and impulse response for further comparison.
Expand the filter transfer function by partial fraction expansion to find the residues of the function at the poles.

H(s)=r_1/(s+100)+r_2/(s+300)

In order to convert the filter using Impulse Invariant by sampling frequency of f_s=1000 Hz (sampling period T=0.001 s), one has to use the following formula for each first order fractions to get the digital filter.

H(z)=(r_1 T)/(1-e^(p_1 T) z^(-1) )+(r_2 T)/(1-e^(p_2 T) z^(-1) )

Combine the fractions to have the final digital filter transfer function:

H(z)=(b_o+b_1 z^(-1))/(1+a_1 z^(-1)+a_2 z^(-2) )

Reference no: EM13264961

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