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Merge pull request #43 from ldeo-glaciology/simplify-deployment
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new build and update deploy.yml
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jkingslake authored Sep 26, 2024
2 parents 0759dbf + fe2d9bc commit 5326c71
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2 changes: 1 addition & 1 deletion .github/workflows/deploy.yml
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# Build the book
- name: Build the book
run: |
jupyter-book build src
jupyter-book build --path-output . src
# Upload the book's HTML as an artifact
- name: Upload artifact
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"metadata": {},
"source": [
"(page:apres-theory)=\n",
"# ApRES theory\n",
"This page describes the theory behind the Autonomous Radio-echo sounder, including \n",
"# Autonomous phase-sensitive radio-echo sounder theory\n",
"This page describes some of the theory behind the Autonomous phase-sensitive radio-echo (ApRES) sounder, including \n",
"- a description of the linear chirps the system emits, \n",
"- how individual and multiple reflectors are represented in the returned signal,\n",
"- how the range to these reflectors is encoded in the frequency content of returned signal, and \n",
"- how to extract the range to reflectors using a fourier transform. "
"- how the range to these reflectors is encoded in the frequency content of the returned signal, and \n",
"- how to extract the range to reflectors using a fourier transform. \n",
"- \n",
"Later pages will describe how the phase information in the returned signal to compute the displacement of reflectors. "
]
},
{
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"metadata": {},
"outputs": [],
"source": [
"s = np.exp(1j*2*np.pi*f_d*t)"
"s = np.exp(1j*2*np.pi*f_d*t) "
]
},
{
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"source": [
"This range-amplitude plot is the ApRES equivalent of the usual time domain plot you would get from an impulse radar system: i.e. one which sends out a single pulse of radio-wave energy and records the echo from the reflector(s) beneath. \n",
"\n",
"As expected, in the plot above we see a peak at 110 m. We can detect the position of the peak using `argrelextrema`, a function from the pckage `scipy`. "
"As expected, in the plot above we see a peak at 110 m. We can detect the position of the peak using `argrelextrema`, a function from the package `scipy`. "
]
},
{
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"N = f_d T.\n",
"$$\n",
"\n",
"The more cycles in a signal, the more precisely the fourier transform can determine its frequency. This is a fundamental property of fourier transforms and its crops up in many applications, including in quantum mechanics as the Heisenberg uncertainty principle. This is a great video on the subject from the same source as the video linked above about fouier transforms: https://www.youtube.com/watch?v=MBnnXbOM5S4. This video graphically demonstrates the idea that it is difficult for a foufier transform to determine the frequency of a short signal containing few cycles.\n",
"The more cycles in a signal, the more precisely the fourier transform can determine its frequency. This is a fundamental property of fourier transforms and its crops up in many applications, including in quantum mechanics as the Heisenberg uncertainty principle. This is a great video on the subject from the same source as the video linked above about fourier transforms: https://www.youtube.com/watch?v=MBnnXbOM5S4. This video graphically demonstrates the idea that it is difficult for a fourier transform to determine the frequency of a short signal containing few cycles.\n",
"\n",
"Interestingly, you will notice if you play around with the numbers in the cell above, that (all else being equal) the width of the peak does not depend on the chirp duration, $T$. At first sight this is surprising because you would expect that a longer duration chirp would contain more cycles and would therefore result in a narrower peak. However, notice that as you vary $T$, the number of cycles, which is printed out beneath the cell, does not change. This is because increasing $T$ while keeping $B$ constant decreases the rate of change of the frequency, $K$. This means that by the time the signal arrives back at the radar, the transmitted signal has not increased as much as it would have done if $K$ were larger. Therefore the frequency of the deramped signal, $f_d$, is lower than it would have been. \n",
"Interestingly, you will notice that if you play around with the numbers in the cell above (all else being equal) the width of the peak does not depend on the chirp duration, $T$. At first sight this is surprising because you would expect that a longer duration chirp would contain more cycles and would therefore result in a narrower peak. However, notice that as you vary $T$, the number of cycles, which is printed out beneath the cell, does not change. This is because increasing $T$ while keeping $B$ constant decreases the rate of change of the frequency, $K$. This means that by the time the signal arrives back at the radar, the transmitted signal has not increased as much as it would have done if $K$ were larger. Therefore the frequency of the deramped signal, $f_d$, is lower than it would have been. \n",
"\n",
"A longer chirp duration tends to increase the number of cycles per chirp, but the decrease in frequency of the deramped signal $f_d$ counteracts this. In fact, the two effects balance exactly, resulting in the number of cycles per chirp being independent of $T$. \n",
"\n",
Expand All @@ -659,7 +661,7 @@
"N = B\\tau.\n",
"$$\n",
"\n",
"From this we can see how the badnwidth $B$ effects the peak width, while $T$ does not; $T$ cancelling out in the last step above corresponds to the two effects descrbed above balancing each other exactly. "
"From this we can see how the bandwidth $B$ effects the peak width, while $T$ does not; $T$ cancelling out in the last step above corresponds to the two effects descrbed above balancing each other exactly. "
]
},
{
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"cell_type": "markdown",
"metadata": {},
"source": [
"So far we have considered just one reflectors. In general we simultaneously receive signals from reflectors at a whole range of depths. To give a feel for what this looks like, we will plot the frequency of ten signals with their delays selected randomly, to represent signals from ten reflectors at different depths. "
"So far we have considered just one reflector. In general we simultaneously receive signals from reflectors at a whole range of depths. To give a feel for what this looks like, we will plot the frequency of ten signals with their delays selected randomly, to represent signals from ten reflectors at different depths. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First let's redfine a few functions to make sure to avoid any issues with varied parameter from the previous section."
"First let's redefine a few functions to make sure to avoid any issues caused by varying parameters in the previous section."
]
},
{
Expand All @@ -698,6 +700,8 @@
"f_2 = 400e6 # ending frequency\n",
"f_c = (f_1+f_2)/2 # center frequency\n",
"B = f_2 - f_1 # bandwidth\n",
"K = B/T # [Hz/s]\n",
"\n",
"sampling_frequency = 40000 # [Hz]\n",
"t = np.linspace(0,T,sampling_frequency*T) # time vector\n",
"def chirp(delay = 0):\n",
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"cell_type": "markdown",
"metadata": {},
"source": [
"In practice, signals from all the reflectors are combined togather and arrive back at the radar simultaneously, thoughout the chirp. This means that the signal received by the radar is the sum of signals reflected by many reflectors - hundreds or thousands in reality, compared to the ten we plotted above. Moreover, the signals all have slightly different frequencies differences, $f_d$, depending on the range to each reflector. Let's generate the deramped signal that these ten reflectors would yield and plot it. \n",
"In practice, signals from all the reflectors are combined together and arrive back at the radar simultaneously, thoughout the chirp. This means that the signal received by the radar is the sum of signals reflected by many reflectors - hundreds or thousands in reality, compared to the ten we plotted above. Moreover, the signals all have slightly different frequencies differences, $f_d$, depending on the range to each reflector. Let's generate the deramped signal that these ten reflectors would yield and plot it. \n",
"\n",
"We first compute the frequency differences for each reflector:"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"The plot above shows what ApRES would record to disk if in our simple 10-reflector case. The signal has ten frequency components, each correspondong to one reflector. The challenge now is to estimate these frequency componets to determine the range to all the reflectors. As above, we use a fourier transform. "
"The plot above shows what ApRES would record to disk in our simple 10-reflector case. The signal has ten frequency components, each correspondong to one reflector. The challenge now is to estimate these frequency componets to determine the range to all the reflectors. As above, we use a fourier transform. "
]
},
{
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"cell_type": "markdown",
"metadata": {},
"source": [
"12. Summary\n",
"## 12. Summary\n",
"- ApRES emits one-second-long chirps. \n",
"- ApRES detects the range to sub-surface reflectors by combined the frequency of a transmitted signal, which continually increases throughout each chirp, to the frequency of the signal received from the reflectors. \n",
"- The tranmistted and received signal are in the MHz range. \n",
"- This combination results in a 'deramped' signal which is in the audio frequency range.\n",
"- The deramped signal is saved to disk by ApRES. \n",
"- The frequency components of the deramped signal are extracted using a fourier transform to determine the range to sub-surface reflectors.\n",
"- The range-amplitude results, `S`, can be used to compute deisplacement of reflectors using cross-correlation betweeen successive measurements."
"\n",
"On the next page we explore the beat frequency and how it help us estiamte difference between the frequncies of the transmitted and received signals. \n"
]
},
{
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},
"nbformat": 4,
"nbformat_minor": 4
}
}
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<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="sections/radar/impulse/impulse-radar.html">Impulse Radar</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="sections/radar/apres/apres-intro.html">Autonomous phase-sensitive Radio Echo Sounder</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/theory_1.html">ApRES theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/theory_1.html">Autonomous phase-sensitive radio-echo sounder theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/beat-frequency.html">Beat frequency</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/stacking.html">Stacking ApRES data</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/apres_data_1.html">A first look at ApRES data</a></li>
</ul>
</li>
</ul>
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<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="sections/radar/impulse/impulse-radar.html">Impulse Radar</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="sections/radar/apres/apres-intro.html">Autonomous phase-sensitive Radio Echo Sounder</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/theory_1.html">ApRES theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/theory_1.html">Autonomous phase-sensitive radio-echo sounder theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/beat-frequency.html">Beat frequency</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/stacking.html">Stacking ApRES data</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/apres_data_1.html">A first look at ApRES data</a></li>
</ul>
</li>
</ul>
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<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="sections/radar/impulse/impulse-radar.html">Impulse Radar</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="sections/radar/apres/apres-intro.html">Autonomous phase-sensitive Radio Echo Sounder</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/theory_1.html">ApRES theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/theory_1.html">Autonomous phase-sensitive radio-echo sounder theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/beat-frequency.html">Beat frequency</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/stacking.html">Stacking ApRES data</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/apres_data_1.html">A first look at ApRES data</a></li>
</ul>
</li>
</ul>
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4 changes: 2 additions & 2 deletions src/_build/html/search.html → _build/html/search.html
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<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="sections/radar/impulse/impulse-radar.html">Impulse Radar</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="sections/radar/apres/apres-intro.html">Autonomous phase-sensitive Radio Echo Sounder</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/theory_1.html">ApRES theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/theory_1.html">Autonomous phase-sensitive radio-echo sounder theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/beat-frequency.html">Beat frequency</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/stacking.html">Stacking ApRES data</a></li>
<li class="toctree-l2"><a class="reference internal" href="sections/radar/apres/apres_data_1.html">A first look at ApRES data</a></li>
</ul>
</li>
</ul>
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<link rel="index" title="Index" href="../../genindex.html" />
<link rel="search" title="Search" href="../../search.html" />
<link rel="next" title="Bibliography" href="../../bibliography.html" />
<link rel="prev" title="Stacking ApRES data" href="../radar/apres/stacking.html" />
<link rel="prev" title="A first look at ApRES data" href="../radar/apres/apres_data_1.html" />
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<meta name="docsearch:language" content="en"/>
</head>
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<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="../radar/impulse/impulse-radar.html">Impulse Radar</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../radar/apres/apres-intro.html">Autonomous phase-sensitive Radio Echo Sounder</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/theory_1.html">ApRES theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/theory_1.html">Autonomous phase-sensitive radio-echo sounder theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/beat-frequency.html">Beat frequency</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/stacking.html">Stacking ApRES data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/apres_data_1.html">A first look at ApRES data</a></li>
</ul>
</li>
</ul>
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<!-- Previous / next buttons -->
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<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="../radar/impulse/impulse-radar.html">Impulse Radar</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../radar/apres/apres-intro.html">Autonomous phase-sensitive Radio Echo Sounder</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/theory_1.html">ApRES theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/theory_1.html">Autonomous phase-sensitive radio-echo sounder theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/beat-frequency.html">Beat frequency</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/stacking.html">Stacking ApRES data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/apres_data_1.html">A first look at ApRES data</a></li>
</ul>
</li>
</ul>
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<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="../radar/impulse/impulse-radar.html">Impulse Radar</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../radar/apres/apres-intro.html">Autonomous phase-sensitive Radio Echo Sounder</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/theory_1.html">ApRES theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/theory_1.html">Autonomous phase-sensitive radio-echo sounder theory</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/beat-frequency.html">Beat frequency</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/stacking.html">Stacking ApRES data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../radar/apres/apres_data_1.html">A first look at ApRES data</a></li>
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