Question

by the differential equation What is the frequency response of the stable, causal LTI system defined by the differential equation: dy(t) dy(t) dt dt dt Use Matlab syntax for your response, assuming w is the frequency vector

Answer 1

first convert difference equation to transfer function form,

apply laplase transform to difference equation

$s^{2}Y(s)+6*s*Y(s)+2*Y(s)=s*X(s)+4*X(s)$

$(s^{2}+6s+2)*Y(s)=(s+4)*X(s)$$\frac{Y(s)}{X(s)}=\frac{(s+4)}{(s^{2}+6s+2)}$

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)