Matrix convulsion in the x,y plane with intersections

Hello all. I need help regarding the intersection point between a freqs plot and yline plotted on the same plot. How can I go about doing this? I'll leave a portion of the code below,

[b,a] = butter(8,[omegac1 omegac2],'bandpass','s');

figure; freqs(b,a) Gp=0.8881779763; yline(Gp,'Gp');

I need the intersection point (x,y) between yline(gp) and the freqs figure from above. I'd appreciate any help. Thanks in advance.

[Star Strider]

@USER SEEF — Please do not eliminate the question, especially after someone has gone through the trouble of posting an Answer.

The question text had to do with determining the frequency at which a transfer function intersected a yline at 9.68. This is similar to Bode plot for Simulink presentation.

I will not delete my Answer.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Star Strider]

Again using the same example from the documentation —

a = [1 0.4 1];
b = [0.2 0.3 1];
w = logspace(-1,1.3);

h = freqs(b,a,w);
fp = 9.68;
hfp = freqs(b,a,[1;1]*fp)

hfp = 
   0.1923 - 0.0233i
   0.1923 - 0.0233i

mag = abs(h);
phase = angle(h);
phasedeg = phase*180/pi;
Gp=0.8881779763;
idx = find(diff(sign(mag-Gp)));                                     % Approximate Indes
wint = interp1(mag([-1:1]+idx),w([-1:1]+idx), Gp)                   % Interpolated Frequency Value

wint = 1.3077

magint = freqs(b,a,[1;1]*wint)                                      % Interpolated MAgnitude Value

magint = 
  -0.3369 - 0.8008i
  -0.3369 - 0.8008i

subplot(2,1,1)
loglog(w,mag)
hold on
plot(fp, abs(hfp(1)),'+r')
plot(wint,abs(magint(1)),'rs')
hold off
grid on
xlabel('Frequency (rad/s)')
ylabel('Magnitude')
yline(Gp,'-g','Gp');
text(wint,abs(magint(1)), sprintf('  \\leftarrow Intersection %.3f rad/s',wint), 'Horiz','left', 'Vert','middle', 'Rotation', -10)

subplot(2,1,2)
semilogx(w,phasedeg)
hold on
plot(fp, rad2deg(angle(hfp(1))),'+r')
plot(wint,rad2deg(angle(magint(1))),'rs')
hold off
grid on
xlabel('Frequency (rad/s)')
ylabel('Phase (degrees)')
text(wint,rad2deg(angle(magint(1))), sprintf('  \\leftarrow Intersection %.3f rad/s',wint), 'Horiz','left', 'Vert','middle', 'Rotation', 10)

Experiment to get different results.

.