Correct unit of curves and scalling

huddle-test-geophones/index.org

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