FROM THE TABLE PLEASE SOLVE FOR FILTERS 1 - 9

Filters zero (cartesian) pole (cartesian) filter real imaginary real imaginary -1 0.95 2 -0.95 3+1 +0.95i +0.95 5'-1 ti,+1/v2i/v2 1 11,-1/2/12 +1/+2+i/v2 ti,+1/V2+i/12 zero (polar) a zero (polar) r pole (polar) a pole (polar) 0.6283 0.7854 1.0472 3.1416 2.0944 0.6283 0.98 0.7854 0.98 2.0944 0.98 0.6283 0.75 0.7854 0.75 2.0944 0.75 For the filters above H(z)= x(2) Prelab i. Derive the transfer function expression in terms of the zero and pole polynomials Y(z) zero polynomial X(2) pole polynomial Find bo such that the maximum gain of the filter (angle om) is 1, that is, H lem = 1 iii. Plot the pole-zero diagram. Plot the magnitude and phase response (HO), ZHO).. Find an expression for the discrete time difference equation for y(n). Draw the network structure in direct form II. vii. Plot y(n) and x(n) overlaid for x(n) = cos(n21/16), cos(n27/8) and cos(n2T/4). V. Filters zero (cartesian) pole (cartesian) filter real imaginary real imaginary -1 0.95 2 -0.95 3+1 +0.95i +0.95 5'-1 ti,+1/v2i/v2 1 11,-1/2/12 +1/+2+i/v2 ti,+1/V2+i/12 zero (polar) a zero (polar) r pole (polar) a pole (polar) 0.6283 0.7854 1.0472 3.1416 2.0944 0.6283 0.98 0.7854 0.98 2.0944 0.98 0.6283 0.75 0.7854 0.75 2.0944 0.75 For the filters above H(z)= x(2) Prelab i. Derive the transfer function expression in terms of the zero and pole polynomials Y(z) zero polynomial X(2) pole polynomial Find bo such that the maximum gain of the filter (angle om) is 1, that is, H lem = 1 iii. Plot the pole-zero diagram. Plot the magnitude and phase response (HO), ZHO).. Find an expression for the discrete time difference equation for y(n). Draw the network structure in direct form II. vii. Plot y(n) and x(n) overlaid for x(n) = cos(n21/16), cos(n27/8) and cos(n2T/4). V