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    "# Input"
   ]
  },
  {
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   "source": [
    "Here you can download the input files (right click / save as...):\n",
    "* <a href=_static/2024-06-07-16k.in download>2024-06-07</a>\n",
    "* <a href=_static/2024-06-06-16k.in download>2024-06-06</a>\n",
    "* <a href=_static/2024-03-16-16k.in download>2024-03-16</a>\n",
    "* <a href=_static/2023-04-20-16k.in download>2023-04-20</a>\n",
    "* <a href=_static/2023-06-15-16k.in download>2023-06-15</a>\n",
    "* <a href=_static/2024-03-14-16k.in download>2023-03-14</a>"
   ]
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    "In this project, we work with audio data.\n",
    "To facilitate reading it into your program, we provide the inputs in a simple format:\n",
    "\n",
    "```{admonition} Format\n",
    "The first line contains $n$, the number of samples ($0 \\leq n < 2^{32}$).\n",
    "\n",
    "Afterwards, $n$ lines follow, each with one sample $x$ as an integer ($-2^{15} \\leq x < 2^{15}$).\n",
    "```\n",
    "\n",
    "The sampling rate $f_s$ is fixed at 16640 Hz.\n",
    "\n",
    "## Example\n",
    "```\n",
    "10\n",
    "623\n",
    "-310\n",
    "-273\n",
    "3404\n",
    "4745\n",
    "655\n",
    "-454\n",
    "3463\n",
    "3375\n",
    "-5350\n",
    "```\n",
    "\n",
    "```{note}\n",
    "Although the samples are given as integer numbers, for the rest of the project it makes sense to convert them into a floating point format at this point already.\n",
    "```"
   ]
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   "source": [
    "# Visualization\n",
    "\n",
    "It can be helpful during this project to visualize the result after every step.\n",
    "Wen can do this for example like this:\n",
    "- The signal contains 2 lines with 2080 pixels each per second. With $f_S = 16640\\text{Hz}$, we have 4 samples per pixel.\n",
    "- We take every 4th sample. For complex numbers, we calculate the magnitude $(a + ib \\mapsto \\sqrt{a^2+b^2} =\\mathrel{\\vcenter{:}} v)$.\n",
    "- We find $v_{min}$ and $v_{max}$, the smallest and largest values we obtained.\n",
    "  Then we scale each $v$ to $255 \\cdot (v - v_{min}) / (v_{max} - v_{min})$.\n",
    "  The result is a value between 0 and 255.\n",
    "- We can save these values as pixels in an image file.\n",
    "  To do this, we can use the [](pgm-format) for example.\n",
    "  \n",
    "```{figure} img/reference/raw_full_scaled.webp\n",
    "---\n",
    "name: fig:raw_full.en\n",
    "---\n",
    "Visualization, directly after reading the input.\n",
    "The image can be discerned already, but it is quite dark.\n",
    "```\n",
    "\n",
    "```{figure} img/reference/raw_detail.webp\n",
    "---\n",
    "name: fig:raw_detail.en\n",
    "---\n",
    "Detail view.\n",
    "We can clearly see vertical lines, stemming from the modulation onto the 2.4 kHz carrier.\n",
    "```"
   ]
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