close all
clear
Fdsp  = 2.4e6;
% can place resonator +/- Fdsp/2
fres  = 300e3;
fnorm = fres/Fdsp;

z0 = 0.98*exp(1j*2*pi*fnorm);
p0 = 0.95*exp(1j*2*pi*(fnorm+0.002));
b = [1, -z0];
a = [1, -p0];
fvtool([1, -z0], [1, -p0], 'Fs', Fdsp)

theta = 0.5;  % arbitrary phase offset, rad
tau   = 1e-9; % 1 ns delay

% digital frequency -- -pi to pi maps to -Fs/2 to Fs/2
w = linspace(-pi, pi, 2^13);
f = w*Fdsp/2/pi;                          % frequencies in Hz

[s21, w] = freqz(b, a, w);                % resonator S21
s21 = s21.*exp(-1j*theta);                % apply arb phase offset
s21 = s21.*exp(-1j*2*pi*f*tau);           % apply time delay

figure
subplot(2,1,1)
plot(f, 20*log10(abs(s21)), 'LineWidth', 2)
title('Resonator Transfer Function', 'FontSize', 12)
grid minor
xlabel('Frequency', 'FontSize', 12)
ylabel('Magnitude (dB)', 'FontSize', 12)

subplot(2,1,2)
plot(f, unwrap(angle(s21)), 'LineWidth', 2)
grid minor
xlabel('Frequency', 'FontSize', 12)
ylabel('Phase (rad)', 'FontSize', 12)

figure
plot(real(s21(1:10:end)), imag(s21(1:10:end)), '.', 'LineWidth', 2)
grid minor
title('S_{21}', 'FontSize', 12)
xlabel('Real S_{21}', 'FontSize', 12)
ylabel('Imag S_{21}', 'FontSize', 12)

%% Here's the real test -- move the resonator and see how it responds
apply_eta  = @(x, eta_offset, eta) (x + eta_offset)*eta;

% can place resonator +/- Fdsp/2
dfres = 1e3; % move the resonator from it's original frequency
fres  = 300e3 + dfres;
fnorm = fres/Fdsp;

z0 = 0.98*exp(1j*2*pi*fnorm);
p0 = 0.95*exp(1j*2*pi*(fnorm+0.002));
b = [1, -z0];
a = [1, -p0];

[s21, w] = freqz(b, a, w);                  % resonator S21
s21 = s21.*exp(-1j*theta);                  % apply arb phase offset
s21 = s21.*exp(-1j*2*pi*tau*f);             % apply time delay
s21_eta  = apply_eta(s21, eta_offset, eta); % apply eta

disp(['We moved the resonator ', num2str(dfres), 'Hz and measured ', num2str(round(imag(s21_eta(ftone)))), ' Hz error'])

>> We moved the resonator 1000Hz and measured -984 Hz error