Add ASD of displacement

huddle-test-geophones/index.org

@@ -149,14 +149,14 @@ The amplifiers also include a low pass filter with a cut-off frequency set at 1k
 #+begin_src matlab :results none
   G0 = 60; % [dB]
 
-  G = G0/(1+s/2/pi/1000);
+  G = 10^(G0/20)/(1+s/2/pi/1000);
 #+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 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, f, 'Hz')))./squeeze(abs(freqresp(S, f, 'Hz')));
+  scaling = 1./squeeze(abs(freqresp(G*S, f, 'Hz')));
 #+end_src
 
 ** Computation of the ASD of the velocity
@@ -165,8 +165,8 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
 #+begin_src matlab :results none
   figure;
   hold on;
-  plot(f, sqrt(pxx1)./scaling);
+  plot(f, sqrt(pxx1).*scaling);
-  plot(f, sqrt(pxx2)./scaling);
+  plot(f, sqrt(pxx2).*scaling);
   hold off;
   set(gca, 'xscale', 'log');
   set(gca, 'yscale', 'log');
@@ -176,7 +176,7 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
 
 #+NAME: fig:psd_velocity
 #+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/psd_velocity.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+#+begin_src matlab :var filepath="figs/psd_velocity.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
   <<plt-matlab>>
 #+end_src
 
@@ -185,6 +185,30 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
 #+RESULTS: fig:psd_velocity
 [[file:figs/psd_velocity.png]]
 
+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);
+  hold off;
+  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
+  xlim([2, 500]);
+#+end_src
+
+#+NAME: fig:asd_displacement
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/asd_displacement.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:asd_displacement
+#+CAPTION: Amplitude Spectral Density of the displacement as measured by the geophones
+#+RESULTS: fig:asd_displacement
+[[file:figs/asd_displacement.png]]
+
 ** Transfer function between the two geophones
 We here compute the transfer function from one geophone to the other.
 The result is shown on figure [[fig:tf_geophones]].

huddle-test-geophones/signal_processing.m

@@ -80,7 +80,7 @@ ylabel('Amplitude [V/(m/s)]')
 
 G0 = 60; % [dB]
 
-G = G0/(1+s/2/pi/1000);
+G = 10^(G0/20)/(1+s/2/pi/1000);
 
 
 
@@ -88,7 +88,7 @@ G = G0/(1+s/2/pi/1000);
 % We further divide the result by the sensibility of the Geophone to obtain the ASD of the velocity in $m/s/\sqrt{Hz}$.
 
 
-scaling = 1./squeeze(abs(freqresp(G, f, 'Hz')))./squeeze(abs(freqresp(S, f, 'Hz')));
+scaling = 1./squeeze(abs(freqresp(G*S, f, 'Hz')));
 
 % Computation of the ASD of the velocity
 % The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
@@ -96,14 +96,33 @@ scaling = 1./squeeze(abs(freqresp(G, f, 'Hz')))./squeeze(abs(freqresp(S, f, 'Hz'
 
 figure;
 hold on;
-plot(f, sqrt(pxx1)./scaling);
+plot(f, sqrt(pxx1).*scaling);
-plot(f, sqrt(pxx2)./scaling);
+plot(f, sqrt(pxx2).*scaling);
 hold off;
 set(gca, 'xscale', 'log');
 set(gca, 'yscale', 'log');
 xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
 xlim([2, 500]);
 
+
+
+% #+NAME: fig:psd_velocity
+% #+CAPTION: Spectral density of the velocity
+% #+RESULTS: fig:psd_velocity
+% [[file:figs/psd_velocity.png]]
+
+% We also plot the ASD in displacement (figure [[fig:asd_displacement]]);
+
+
+figure;
+hold on;
+plot(f, (pxx1.*scaling./f).^2);
+plot(f, (pxx2.*scaling./f).^2);
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
+xlim([2, 500]);
+
 % Transfer function between the two geophones
 % We here compute the transfer function from one geophone to the other.
 % The result is shown on figure [[fig:tf_geophones]].