#+end_export
* Introduction :ignore:
Because of the lack of a large anechoic room or a near field scanner system (e.g. the [[http://www.klippel.de/products/rd-system/modules/nfs-near-field-scanner.html#:~:text=The%20Near-Field%20Scanner%203D,move%20during%20the%20scanning%20process.][Klippel NFS]]), the low frequency and high frequency response of the speaker have to be measured separately.
- Section [[sec:equipment]]: the tools used for the measurements are listed
- Section [[sec:outdoor_meas]]: the high frequency behavior of the speaker is measured with a semi-anechoic measurement performed outdoors
- Section [[sec:ground_plane_meas]]: the low frequency behavior of the speaker is measured using the "ground plane technique"
- Section [[sec:in_room_meas]]: the response of the speaker in a typical room is estimated from the two above measurements and compare with in-room measurements
* Equipment
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- REW software ([[https://www.roomeqwizard.com/][link]])
- Audiobox USB ([[https://www.presonus.com/products/audiobox-usb][link]])
- Behringer ECM 8000 Measuring microphone
- TOPPING D70 DAC
- Power amplifier: Amplifier
* Semi-Anechoic Outdoor measurement
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** Introduction :ignore:
The frequency resolution is limited by the time difference between the direct sound and the first reflection.
If we note $\tau$ this time difference, the frequency resolution $\delta f$ is:
\begin{equation}
\delta f = \frac{1}{\tau}
\end{equation}
with $\delta f$ in hertz and $\tau$ in seconds.
A schematic of the setup is shown in Figure [[fig:outside_meas_setup]].
#+name: fig:outside_meas_setup
#+caption: Schematic of the setup
[[file:figs/outside_meas_setup.png]]
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<>
#+end_src
** Analysis :ignore:
We usually want to measure the speaker with a resonable distance.
Let's take $L = 2\,m$.
#+begin_src matlab
L = 2; % Distance speaker/microphone [m]
v = 340; % Speed of sound [m/s]
#+end_src
We can then compute the time delay $\tau$ between the direct sound and reflected sound as a function of the height $H$.
Similarly, we can compute the frequency resolution $\delta f$ as a function of $H$.
Both are shown in Figure [[fig:required_height_wanted_reflection_delay]].
#+begin_src matlab
H = [0:0.01:4]; % [m]
D = 2*sqrt(H.^2 + L^2/4); % [m]
tau = (D - L)/v; % [s]
#+end_src
#+begin_src matlab :exports none
figure;
yyaxis left
plot(H, 1000*tau)
ylabel('Reflection Time $\tau$ [ms]');
yyaxis right
plot(H, 1./tau);
ylabel('Frequency Resolution $\delta f$ [Hz]');
set(gca, 'yscale', 'log');
ylim([1e1, 1e3]);
xlabel('Height $H$ [m]');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/required_height_wanted_reflection_delay.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:required_height_wanted_reflection_delay
#+caption: Time delay $\tau$ between the direct sound and (first) reflected sound as a function of the height $H$. The resulting frequency resolution $\delta f$ is also shown.
#+RESULTS:
[[file:figs/required_height_wanted_reflection_delay.png]]
#+begin_important
It is shown than even for high heights ($H = 3\,m$), the frequency resolution will be quite poor for low frequency characterisation of the speaker ($\delta f \approx 70\,Hz$).
However, it is much sufficient for high frequency characterisation of the speaker (say above 500Hz).
#+end_important
The speaker can then be tilted horizontally and vertically as shown in Figure [[fig:outside_meas_setup_tilt_vert]] and [[fig:outside_meas_setup_tilt_hor]].
#+name: fig:outside_meas_setup_tilt_vert
#+caption: Tilting the speaker around a vertical axis
[[file:figs/outside_meas_setup_tilt_vert.png]]
#+name: fig:outside_meas_setup_tilt_hor
#+caption: Tilting the speaker around a horizontal axis
[[file:figs/outside_meas_setup_tilt_hor.png]]
* Ground Plane Technique
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** Introduction :ignore:
The idea here is to put both the microphone and the speaker on the ground.
The ground must be relatively stiff.
#+name: fig:ground_plane_meas_setup
#+caption: Schematic of the measurement setup
[[file:figs/ground_plane_meas_setup.png]]
It is then possible to use very large gate windows in order to identify the low frequency behavior of the speaker.
It is here not useful to perform any off-axis measurements as at the frequencies, the speaker is perfectly omnidirectionnal.
* In room measurement
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- [ ] Estimated response
- [ ] Correlation with measurement