What is the frequency response of the stable, causal LTI system defined by the differential equation:fraction numerator d squared y (t )over denominator d t squared end fraction plus 6 fraction numerator d y (t )over denominator d t end fraction plus 2 y (t )equals fraction numerator d x (t )over denominator d t end fraction plus 4 x (t )Use Matlab syntax for your response, assuming w is the frequency vector. Make sure you use parentheses correctly (try plotting your code in Matlab)

Explanation:

first convert difference equation to transfer function form,

apply laplase transform to difference equation

s2Y(s) + 6 * s * y(s) + 2 * y(s) = s * X(s) + 4 * X(s)

(s2 + 6s+2) * y(s) = (s+4)*X(s)Y s)

Lets write below code in matlab command prompt

lets use lodspace to create values from 10^-1 to 10^5 and use freqs to plot frequency response of above system with frequency w

>> n=[1 4];

>> d=[1 6 2];

>> w = logspace(-1,5);

>> freqs(n,d,w)

Attached is the written solution and the MATLAB diagram

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answer:

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