Use MATLAB to calculate Laplace Transform ind inverse Laplace Transform. Provide the results and the snapshot of the code used.
a) Calculate the Laplace Transform of the following signal [cos(3t)e⁻²ᵗ+5 sin(3t)e⁻²ᵗ]u(t)
b) Calculate the inverse Laplace Transform of the following (this is actually the transfer function of a typical 3ʳᵈ order low-pass Butterworth filter.)
1/(s+1)(s²+s+1)
c) Calculate the inverse Laplace Transform of the following (this is actually the transfer function of a 1ˢᵗ order high-pass filter.)
s/s+1