4.1 Theoretical work (to be done before the lab session) Second-order LTI systems (modeled by 2nd order linear differential equation with constant coefficients) are popular devices in signal processing. For example, many typical filters are actually 2nd order LTI systems. In this experiment, we consider two exemplary models of such systems: a) /(0)+1.2yt)+ (t)=1.2x(t) b) y"(t)+1.2 y'(t)+ y(t)=x"(t)+x(t) I. Find the natural response of both systems. You can use MATLAB symbolic calculations (dsolve command - see MATLAB help) as a help. Consider two cases of the initial conditions: i. y0)=l and y'(0)=0.2 ii. y(O)=() and y'(O)=0.8 Find the Fourier frequency response and the Laplace transfer function for both systems. You can use MATLAB symbolic calculations as a help. II. III. IV. Find the impulse response equations for both systems. You can use MATLAB symbolic calculations as a help. Using the Laplace transfer functions, find the forced responses of both systems to inputs xi(t)=sin(t) , xz(t)=sin(0.lt) and xz(t)=sin(10t). You can use MATLAB symbolic calculations as a help. 4.1 Theoretical work (to be done before the lab session) Second-order LTI systems (modeled by 2nd order linear differential equation with constant coefficients) are popular devices in signal processing. For example, many typical filters are actually 2nd order LTI systems. In this experiment, we consider two exemplary models of such systems: a) /(0)+1.2yt)+ (t)=1.2x(t) b) y"(t)+1.2 y'(t)+ y(t)=x"(t)+x(t) I. Find the natural response of both systems. You can use MATLAB symbolic calculations (dsolve command - see MATLAB help) as a help. Consider two cases of the initial conditions: i. y0)=l and y'(0)=0.2 ii. y(O)=() and y'(O)=0.8 Find the Fourier frequency response and the Laplace transfer function for both systems. You can use MATLAB symbolic calculations as a help. II. III. IV. Find the impulse response equations for both systems. You can use MATLAB symbolic calculations as a help. Using the Laplace transfer functions, find the forced responses of both systems to inputs xi(t)=sin(t) , xz(t)=sin(0.lt) and xz(t)=sin(10t). You can use MATLAB symbolic calculations as a help