Correct unit of curves and scalling
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huddle-test-geophones/figs/asd_voltage.png
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@ -106,29 +106,56 @@ We load the data of the z axis of two geophones.
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** Computation of the ASD of the measured voltage
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** Computation of the ASD of the measured voltage
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We first define the parameters for the frequency domain analysis.
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We first define the parameters for the frequency domain analysis.
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#+begin_src matlab :results none
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#+begin_src matlab :results none
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Fs = 1/dt;
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Fs = 1/dt; % [Hz]
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win = hanning(ceil(10*Fs));
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win = hanning(ceil(10*Fs));
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#+end_src
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#+end_src
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Then we compute the Power Spectral Density using =pwelch= function.
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#+begin_src matlab :results none
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#+begin_src matlab :results none
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[pxx1, f] = pwelch(x1, win, [], [], Fs);
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[pxx1, f] = pwelch(x1, win, [], [], Fs);
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[pxx2, ~] = pwelch(x2, win, [], [], Fs);
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[pxx2, ~] = pwelch(x2, win, [], [], Fs);
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#+end_src
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#+end_src
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And we plot the result on figure [[fig:asd_voltage]].
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(f, sqrt(pxx1));
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plot(f, sqrt(pxx2));
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
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#+end_src
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#+NAME: fig:asd_voltage
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/asd_voltage.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:asd_voltage
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#+CAPTION: Amplitude Spectral Density of the measured voltage
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#+RESULTS: fig:asd_voltage
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[[file:figs/asd_voltage.png]]
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** Scaling to take into account the sensibility of the geophone and the voltage amplifier
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** Scaling to take into account the sensibility of the geophone and the voltage amplifier
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The Geophone used are L22.
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The Geophone used are L22. Their sensibility is shown on figure [[fig:geophone_sensibility]].
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Their sensibility are shown on figure [[fig:geophone_sensibility]].
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#+begin_src matlab :results none
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#+begin_src matlab :results none
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S0 = 88; % Sensitivity [V/(m/s)]
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S0 = 88; % Sensitivity [V/(m/s)]
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f0 = 2; % Cut-off frequnecy [Hz]
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f0 = 2; % Cut-off frequnecy [Hz]
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S = (s/2/pi/f0)/(1+s/2/pi/f0);
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S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
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#+end_src
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#+end_src
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#+begin_src matlab :results none :exports none
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#+begin_src matlab :results none :exports none
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figure;
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figure;
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bodeFig({S});
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bodeFig({S}, logspace(-1, 2, 1000));
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ylabel('Amplitude [V/(m/s)]')
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ylabel('Amplitude $\left[\frac{V}{m/s}\right]$')
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#+end_src
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#+end_src
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#+NAME: fig:geophone_sensibility
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#+NAME: fig:geophone_sensibility
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@ -144,19 +171,18 @@ Their sensibility are shown on figure [[fig:geophone_sensibility]].
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We also take into account the gain of the electronics which is here set to be $60dB$.
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We also take into account the gain of the electronics which is here set to be $60dB$.
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The amplifiers also include a low pass filter with a cut-off frequency set at 1kHz.
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#+begin_src matlab :results none
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#+begin_src matlab :results none
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G0 = 60; % [dB]
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G0_db = 60; % [dB]
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G = 10^(G0/20)/(1+s/2/pi/1000);
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G0 = 10^(60/G0_db); % [abs]
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#+end_src
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#+end_src
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We divide the ASD measured (in $\text{V}/\sqrt{\text{Hz}}$) by the transfer function of the voltage amplifier to obtain the ASD of the voltage across the geophone.
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We divide the ASD measured (in $\text{V}/\sqrt{\text{Hz}}$) by the gain of the voltage amplifier to obtain the ASD of the voltage across the geophone.
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We further divide the result by the sensibility of the Geophone to obtain the ASD of the velocity in $m/s/\sqrt{Hz}$.
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We further divide the result by the sensibility of the Geophone to obtain the ASD of the velocity in $m/s/\sqrt{Hz}$.
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#+begin_src matlab :results none
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#+begin_src matlab :results none
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scaling = 1./squeeze(abs(freqresp(G*S, f, 'Hz')));
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scaling = 1./squeeze(abs(freqresp(G0*S, f, 'Hz')));
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#+end_src
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#+end_src
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** Computation of the ASD of the velocity
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** Computation of the ASD of the velocity
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@ -170,7 +196,7 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
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hold off;
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
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xlabel('Frequency [Hz]'); ylabel('ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
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xlim([0.1, 500]);
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#+end_src
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#+end_src
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@ -181,7 +207,7 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
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#+end_src
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#+end_src
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#+NAME: fig:psd_velocity
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#+NAME: fig:psd_velocity
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#+CAPTION: Spectral density of the velocity
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#+CAPTION: Amplitude Spectral Density of the Velocity
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#+RESULTS: fig:psd_velocity
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#+RESULTS: fig:psd_velocity
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[[file:figs/psd_velocity.png]]
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[[file:figs/psd_velocity.png]]
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@ -190,11 +216,11 @@ We also plot the ASD in displacement (figure [[fig:asd_displacement]]);
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#+begin_src matlab :results none
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#+begin_src matlab :results none
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figure;
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figure;
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hold on;
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hold on;
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plot(f, (pxx1.*scaling./f).^2);
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plot(f, (sqrt(pxx1).*scaling)./(2*pi*f));
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plot(f, (pxx2.*scaling./f).^2);
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plot(f, (sqrt(pxx2).*scaling)./(2*pi*f));
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hold off;
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
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xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
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xlim([0.1, 500]);
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#+end_src
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#+end_src
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@ -205,7 +231,7 @@ We also plot the ASD in displacement (figure [[fig:asd_displacement]]);
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#+end_src
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#+end_src
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#+NAME: fig:asd_displacement
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#+NAME: fig:asd_displacement
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#+CAPTION: Amplitude Spectral Density of the displacement as measured by the geophones
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#+CAPTION: Amplitude Spectral Density of the Displacement
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#+RESULTS: fig:asd_displacement
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#+RESULTS: fig:asd_displacement
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[[file:figs/asd_displacement.png]]
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[[file:figs/asd_displacement.png]]
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@ -232,7 +258,7 @@ We also compute the coherence between the two signals (figure [[fig:coh_geophone
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set(gca, 'xscale', 'log');
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set(gca, 'xscale', 'log');
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ylim([-180, 180]);
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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yticks([-180, -90, 0, 90, 180]);
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xlabel('Frequency [Hz]'); ylabel('Phase');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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linkaxes([ax1,ax2],'x');
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linkaxes([ax1,ax2],'x');
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xlim([0.1, 500]);
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xlim([0.1, 500]);
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@ -338,7 +364,7 @@ The instrumental noise is computed below. The result in V^2/Hz is shown on figur
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plot(f, pxxN, 'k--');
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plot(f, pxxN, 'k--');
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hold off;
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('PSD [$V^2/Hz$]');
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xlabel('Frequency [Hz]'); ylabel('PSD of the measured Voltage $\left[\frac{V^2}{Hz}\right]$');
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xlim([0.1, 500]);
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xlim([0.1, 500]);
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#+end_src
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#+end_src
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@ -362,7 +388,7 @@ This is then further converted into velocity and compared with the ground veloci
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plot(f, sqrt(pxxN).*scaling, 'k--');
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plot(f, sqrt(pxxN).*scaling, 'k--');
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hold off;
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
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xlabel('Frequency [Hz]'); ylabel('ASD of the Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$');
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xlim([0.1, 500]);
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xlim([0.1, 500]);
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#+end_src
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#+end_src
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