Skip to content

Commit 79e61a3

Browse files
committed
Rename time to td in equation labels
Done by the following commands: sed -i "s/time-/td-/" sources/index.rst sed -i "s/time-/td-/" d_wfs/index.rst sed -i "s/time-/td-/" d_nfchoa/index.rst sed -i "s/time-wfs/td-wfs/" d_wfs/index.rst
1 parent 6b9e604 commit 79e61a3

File tree

3 files changed

+26
-26
lines changed

3 files changed

+26
-26
lines changed

d_nfchoa/index.rst

+2-2
Original file line numberDiff line numberDiff line change
@@ -117,15 +117,15 @@ into :eq:`fd-drivingfunction-linear-25d` and exploiting the fact that
117117
Transferred to the temporal domain this results in :cite:`Ahrens2010`, eq. (18)
118118

119119
.. math::
120-
:label: time-sdm-plane-25d
120+
:label: td-sdm-plane-25d
121121
122122
d_{\text{linear},\,\text{2.5D}}(x_0,t) = h(t) *
123123
a\left(t-\frac{x_0}{c}\sin\phi_k-\frac{y_\text{ref}}{c}\sin\phi_k\right),
124124
125125
where :math:`\phi_k` denotes the azimuth direction of the plane wave and
126126

127127
.. math::
128-
:label: time-sdm-prefilter
128+
:label: td-sdm-prefilter
129129
130130
h(t) = {\mathcal{F}^{-1}\left\{\frac{4\i}
131131
{\Hankel{2}{0}{k_y y_\text{ref}}}\right\}}.

d_wfs/index.rst

+20-20
Original file line numberDiff line numberDiff line change
@@ -72,13 +72,13 @@ Transferred to the temporal domain via an inverse Fourier transform :eq:`ifft`,
7272
it follows
7373

7474
.. math::
75-
:label: time-wfs-plane
75+
:label: td-wfs-plane
7676
7777
d(\x_0,t) = 2 a(t) * h(t) * w(\x_0) \scalarprod{\n_k}{\n_{\x_0}}
7878
\dirac{t - \frac{\scalarprod{\n_k}{\x_0}}{c}},
7979
8080
.. math::
81-
:label: time-wfs-plane-25d
81+
:label: td-wfs-plane-25d
8282
8383
\begin{aligned}
8484
d_\text{2.5D}(\x_0,t) =& 2 a(t) * h_\text{2.5D}(t) * w(\x_0)
@@ -90,14 +90,14 @@ it follows
9090
where
9191

9292
.. math::
93-
:label: time-wfs-prefilter
93+
:label: td-wfs-prefilter
9494
9595
h(t) = \mathcal{F}^{-1}\left\{\i\wc \right\},
9696
9797
and
9898

9999
.. math::
100-
:label: time-wfs-prefilter-25d
100+
:label: td-wfs-prefilter-25d
101101
102102
h_\text{2.5D}(t) = \mathcal{F}^{-1}\left\{
103103
\sqrt{\i\wc }\right\}
@@ -228,14 +228,14 @@ The default |WFS| driving functions for a point source in the SFS Toolbox are
228228
temporal domain via an inverse Fourier transform :eq:`ifft` it follows
229229

230230
.. math::
231-
:label: time-wfs-point
231+
:label: td-wfs-point
232232
233233
d(\x_0,t) = \frac{1}{2{\pi}} a(t) * h(t) * w(\x_0)
234234
\frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^2}
235235
\dirac{t-\frac{|\x_0-\xs|}{c}},
236236
237237
.. math::
238-
:label: time-wfs-point-25d
238+
:label: td-wfs-point-25d
239239
240240
\begin{aligned}
241241
d_\text{2.5D}(\x_0,t) =&
@@ -247,7 +247,7 @@ temporal domain via an inverse Fourier transform :eq:`ifft` it follows
247247
\end{aligned}
248248
249249
.. math::
250-
:label: time-wfs-point-25d-refline
250+
:label: td-wfs-point-25d-refline
251251
252252
\begin{aligned}
253253
d_\text{2.5D}(\x_0,t) =&
@@ -349,14 +349,14 @@ transferred to the temporal domain via an inverse Fourier transform :eq:`ifft`
349349
it follows
350350

351351
.. math::
352-
:label: time-wfs-line
352+
:label: td-wfs-line
353353
354354
d(\x_0,t) = \sqrt{\frac{1}{2\pi}} a(t) * h(t) * w(\x0)
355355
\frac{\scalarprod{\vec{v}}{\n_{\x_0}}}{|\vec{v}|^{\frac{3}{2}}}
356356
\dirac{t-\frac{|\vec{v}|}{c}},
357357
358358
.. math::
359-
:label: time-wfs-line-25d
359+
:label: td-wfs-line-25d
360360
361361
d_\text{2.5D}(\x_0,t) =
362362
g_0 \sqrt{\frac{1}{2\pi}} a(t) *
@@ -423,10 +423,10 @@ a diverging one as can be seen in :numref:`fig-wfs-25d-focused-source`. In order
423423
to choose the active secondary sources, especially for circular or spherical
424424
geometries, the focused source also needs a direction :math:`\n_\text{s}`.
425425

426-
The driving function for a focused source is given by the time-reversed
426+
The driving function for a focused source is given by the td-reversed
427427
versions of the driving function for a point source
428-
:eq:`time-wfs-point` and
429-
:eq:`time-wfs-point-25d` as
428+
:eq:`td-wfs-point` and
429+
:eq:`td-wfs-point-25d` as
430430

431431
.. math::
432432
:label: fd-wfs-focused-3d
@@ -435,8 +435,8 @@ versions of the driving function for a point source
435435
\frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^2}
436436
\e{\i\wc |\x_0-\xs|}.
437437
438-
The 2.5D driving functions are given by the time-reversed version of
439-
:eq:`time-wfs-point-25d` for a reference point after
438+
The 2.5D driving functions are given by the td-reversed version of
439+
:eq:`td-wfs-point-25d` for a reference point after
440440
:cite:`Verheijen1997`, eq. (A.14) as
441441

442442
.. math::
@@ -452,7 +452,7 @@ The 2.5D driving functions are given by the time-reversed version of
452452
\end{aligned}
453453
454454
and the time reversed version of
455-
:eq:`time-wfs-point-25d-refline` for a reference line,
455+
:eq:`td-wfs-point-25d-refline` for a reference line,
456456
compare :cite:`Start1997`, eq. (3.16)
457457

458458
.. math::
@@ -475,14 +475,14 @@ Transferred to the temporal domain via an inverse Fourier transform :eq:`ifft`
475475
it follows
476476

477477
.. math::
478-
:label: time-wfs-focused-3d
478+
:label: td-wfs-focused-3d
479479
480480
d(\x_0,t) = \frac{1}{2{\pi}} a(t) * h(t) * w(\x_0)
481481
\frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^2}
482482
\dirac{t+\frac{|\x_0-\xs|}{c}},
483483
484484
.. math::
485-
:label: time-wfs-focused-25d
485+
:label: td-wfs-focused-25d
486486
487487
\begin{aligned}
488488
d_\text{2.5D}(\x_0,t) =&
@@ -494,7 +494,7 @@ it follows
494494
\end{aligned}
495495
496496
.. math::
497-
:label: time-wfs-focused-25d-refline
497+
:label: td-wfs-focused-25d-refline
498498
499499
\begin{aligned}
500500
d_\text{2.5D}(\x_0,t) =&
@@ -505,7 +505,7 @@ it follows
505505
\dirac{t+\frac{|\x_0-\xs|}{c}}.
506506
\end{aligned}
507507
508-
In this document a focused source always refers to the time-reversed version of a
508+
In this document a focused source always refers to the td-reversed version of a
509509
point source, but a focused line source can be defined in the same way starting
510510
from :eq:`fd-wfs-line`
511511

@@ -520,7 +520,7 @@ Transferred to the temporal domain via an inverse Fourier transform :eq:`ifft`
520520
it follows
521521

522522
.. math::
523-
:label: time-wfs-focused-2d
523+
:label: td-wfs-focused-2d
524524
525525
d(\x_0,t) = \sqrt{\frac{1}{2\pi}} a(t) * h(t) * w(\x0)
526526
\frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^{\frac{3}{2}}}

sources/index.rst

+4-4
Original file line numberDiff line numberDiff line change
@@ -63,7 +63,7 @@ where :math:`A(\w)` denotes the frequency spectrum of the source and
6363
Transformed in the temporal domain this becomes
6464

6565
.. math::
66-
:label: time-plane
66+
:label: td-plane
6767
6868
s(\x,t) = a(t) * \dirac{t -\frac{\scalarprod{\n_k}{\x}}{c}},
6969
@@ -149,7 +149,7 @@ where :math:`\xs` describes the position of the point source.
149149
Transformed to the temporal domain this becomes
150150

151151
.. math::
152-
:label: time-point
152+
:label: td-point
153153
154154
s(\x,t) = a(t) * \frac{1}{4\pi} \frac{1}{|\x-\xs|}
155155
\dirac{t - \frac{|\x-\xs|}{c}}.
@@ -237,7 +237,7 @@ directional derivative of the three dimensional Green’s function with respect
237237
Transformed to the temporal domain this becomes
238238

239239
.. math::
240-
:label: time-dipole-point
240+
:label: td-dipole-point
241241
242242
s(\x,t) = a(t) *
243243
\left( \frac{1}{|\x-\xs|} + {\mathcal{F}^{-1}\left\{
@@ -292,7 +292,7 @@ Applying the large argument approximation of the Hankel function
292292
becomes
293293

294294
.. math::
295-
:label: time-line
295+
:label: td-line
296296
297297
s(\x,t) = a(t) * \mathcal{F}^{-1}\left\{\sqrt{
298298
\frac{c}{\i\w}}\right\} * \sqrt{\frac{1}{8\pi}}

0 commit comments

Comments
 (0)