This problem involves an investigation of the effects of roundoff on the location of
the zeros and poles of the system transfer function and on the frequency response
when the system is implemented as a cascade of second-order sections.
Compare the location of the poles and zeros and the frequency response of the resulting filter $\mathrm{H}_2(z)$ to those for the original filter.
(a) Use the Matlab function zplane to compute and plot the poles and zeros for the original floating point coefficients $[b, a]$ and for the scaled coefficients $[b 2, \mathrm{a} 2]$.
(b) Use the Matlab function freqz to compute the magnitude and phase responses for the original floating point coefficients $[b, a]$ and for the scaled coefficients $[\mathrm{b} 2, \mathrm{a} 2]$.