Question: Using two zeroes and two poles to form a high-pass filter with cutoff frequency approximately at Π/3 (-3dB) radian:

a. Plot the placement of pole-zero diagram with the unit circle as the landmark.

b. Sketch the magnitude frequency response.

c. Find the H(z) = B(z)/A(z) with gain at ω = Π, H(-1), normalized to 1.

d. Draw both the direct form II realization and transposed direct form II realization..

e. Find the magnitude and phase frequency response at the frequency ω = Π/3 in dB.

f. Find frequency response H(e^iω) using Matlab function H = freqz(B, A, 24). Plot the magnitude frequency response with a frequency axis: w = 0:pi/24:(24-1)*pi/24;

g. Which sample is corresponding to the frequency response at ω = Π/3? Compare the magnitude and phase values with your calculation from e.