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We can, of course, do the same injections but with the full LPF model and with noise switched on.

In Topic 2 you already saw how to simulate an LPF model with all the noises switched on. If we combine that with the signal injections we've been doing in this topic, then a simulation with noise and injected signals can be done like this:

% Create a standard LPF model lpf = ssm(plist('built-in', 'LPF')); % Generate suitable covariance matrix for all inputs cov = lpf.generateCovariance; % Create some time-series analysis object to inject aSignal = ao(plist('tsfcn', '1e-7*sin(2*pi*0.005*t)', 'fs', 1/lpf.timestep, 'nsecs', 10000)); % Create the plist to configure simulate sim_pl = plist('AOS', aSignal, 'AOS Variable Names', 'GUIDANCE.ifo_x1', ... 'return outputs', {'DELAY_IFO.x1', 'DELAY_IFO.x12'}, ... 'CPSD variable names', cov.find('names'), ... 'CPSD', cov.find('cov')); % Run the simulation out = simulate(lpf, sim_pl);

% Unpack the outputs [o1, o12] = unpack(out); % Plot on subplots plot_pl = plist('arrangement', 'subplots'); iplot(o1, o12, plot_pl);

We can estimate the spectral densities of these two signals and we will should a signal at 5mHz:

% Create a PSD plist with 16 averages, linear segment-wise detrending psd_pl = plist('navs', 16, 'order', 1, 'win', 'BH92'); % Estimate PSDs [o1_xx, o12_xx] = psd(o1, o12, psd_pl); % Plot the ASDs iplot(sqrt(o1_xx), sqrt(o12_xx));

Estimate tranfser functions from simulated signals, compare with Bode estimates | Topic 5 - Introduction to system identification of LPF. |

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