2. Surface plots of Laplace transforms In this exercise, you will visually explore the surfaces defined by rational Laplace transforms and the relationship between the surfaces and the CTFT. Consider

a transfer function: H(s)=\frac{s^2+2s+17}{s^2+4s+104^{}} (1). Define the numerator and denominator polynomial coefficients as vector b and a respectively. (2). Use the freqs function to evaluate the frequency response of a Laplace transform. H = freqs(b, a, Omega); where -20<=w<=20 (omega) is the frequency vector in rad/s. (Hint: use linspace to generate a vector with 200 samples.) (3). Graph the magnitude and phase of the frequency response. (4). Complex number s in the Laplace transform is represented as: s=\sigma+j \mathrm{n} A 3-D surface plot of the system transform function H(s) at the range of interests,i.e. -20<=w<= 20 and, -5<=o<=5 is extremely useful to illustrate the relationship between the frequency response H(s) and the pole-zero locations. the system response matrix s can be generated from w and o using meshgrid function: [sigmagrid, Omegagrid] = meshgrid( sigma, Omega); hence, s-o+ jw is: Sgrid = sigmagrid+j* Omegagrid; use function polyval to evaluate the numerator and denominator polynomials at the specific range: H1 = polyval(b, sgrid)./polyval (a, sgrid); Finally, use mesh() function to generate the surface graph of the magnitude of H(s) in dB: mesh(sigma, Omega, 10*log10 ( abs (H1))) Where are the poles and zeros on the surface plot? What's the relationship between the surface plot and the plot in 2.(2)?