3D-z-plane

# source "H.octave"

function [magnitude, phase] = H(omega, omegac, R)
  # numerator
  N = 1 - e.^(-2 * omega * j);
  # denominator
  D = 1 - 2 * R * cos(omegac) * e.^(-i * omega) + R^2 * e.^(-2 * omega * j);
  F = N ./ D;

  magnitude = abs(F);
  phase     = angle(F);
endfunction

fc = 2.3041E6; # center frequency
fs = 115.2E6;  # sampling frequency
omegac = 2 * pi * fc / fs;

im = [-1:.03:1];
re = [-1:.03:1];

for index_im = 1:size(im,2)
  for index_re = 1:size(re,2)

    c = re(index_re) + i * im(index_im);

    if abs(c) <= 1
      [m,p] = H(angle(c), omegac, abs(c));
      if m > 10
        m = 10;
      endif
    else
      m = -1;
    endif

    mag(index_im, index_re) = m;

  endfor
endfor

hold on
axis([-1, 1, -1, 1, 0, max(max(mag))]);
mesh(re, im, mag)

t = linspace(-pi, pi, 750)';
circle_im = sin(t);
circle_re = cos(t);

c = circle_re + i * circle_im;
[m,p] = H(angle(c), omegac, 0.99);
fig = plot3(circle_re, circle_im, m, "r");
set(fig, "linewidth", 2);

fig = plot(circle_re, circle_im, "k");
set(fig, "linewidth", 2);

hold off