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%% 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