In this problem, we demonstrate that, for a rational z-transform, a factor of the form (z â z0) and a factor of the form z/(z â z*0) contribute the same phase.
(a) Let H(z) = z â 1/a, where a is real and 0 < a=””>< 1.=”” sketch=”” the=”” poles=”” and=”” zeros=”” of=”” the=”” system,=”” including=”” an=”” indication=”” of=”” those=”” at=”” z=”8.” determine=””>< h(ej?),=”” the=”” phase=”” of=”” the=””>
(b) Let G(z) be specified such that it has poles at the conjugate-reciprocal locations of zeros of H(z) and zeros at the conjugate-reciprocal locations of poles of H(z), including those at zero and 8. Sketch the pole-zero diagram of G(z). Determine < g(ej?),=”” the=”” phase=”” of=”” the=”” system,=”” and=”” show=”” that=”” it=”” is=”” identical=”” to=””>< h(ej?),=””>
(a) Let H(z) = z â 1/a, where a is real and 0 < a=””>< 1.=”” sketch=”” the=”” poles=”” and=”” zeros=”” of=”” the=”” system,=”” including=”” an=”” indication=”” of=”” those=”” at=”” z=”8.” determine=””>< h(ej?),=”” the=”” phase=”” of=”” the=””>
(b) Let G(z) be specified such that it has poles at the conjugate-reciprocal locations of zeros of H(z) and zeros at the conjugate-reciprocal locations of poles of H(z), including those at zero and 8. Sketch the pole-zero diagram of G(z). Determine < g(ej?),=”” the=”” phase=”” of=”” the=”” system,=”” and=”” show=”” that=”” it=”” is=”” identical=”” to=””>< h(ej?),=””>
