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   "source": [
    "# RF Exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98a71e06-14df-4093-bc81-cd075778da29",
   "metadata": {},
   "source": [
    "You'll need the following `import`s for the tasks below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af0b284b-41ad-4cc4-aded-a8516a03904a",
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "from ipywidgets import interact, fixed\n",
    "\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4647a59c-047b-46e0-aa5c-ba615b5e36ed",
   "metadata": {},
   "source": [
    "## Task 1 - FFT\n",
    "We start by creating the sum of at least two sinus frequences and plot them."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "406b5f2c-b697-46f0-94a7-f39ccf958c49",
   "metadata": {},
   "source": [
    "Start by creating the sinus curves. Adjust the frequencies as you like from the sample code below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4ce28b67-f975-4eae-9779-c04c16fd4d54",
   "metadata": {},
   "outputs": [],
   "source": [
    "f1 = 0.15 # Hz\n",
    "f2 = 0.5 # Hz\n",
    "t = np.linspace(0, 10, 150)\n",
    "s = np.sin(f1*2*np.pi*t) + np.sin(f2*2*np.pi*t)\n",
    "plt.plot(t, s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8ed5179-4791-4188-b836-513e811b33ee",
   "metadata": {},
   "source": [
    "Now it's up to you to use fft to transform the sinus from the time domain to the\n",
    "frequency domain and plot again. Can you see the frequencies you've created?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51a71a83-068b-412b-acce-ab127deba9a7",
   "metadata": {},
   "source": [
    "## Task 2 - IQ Sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4bd2838-c906-4df9-8978-94e77056e33b",
   "metadata": {},
   "source": [
    "The function below takes the amplitude I of the in-phase component, a frequency and a number of samples. It plots a graphic representation of the in-phase component with the given parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d99659ec-68a9-4014-b536-af7e38384f4b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def iq_plot(I, frequency=0.2, samples=150):\n",
    "    t = np.linspace(0, 10, samples)\n",
    "    i_s = I * np.cos(2 * np.pi * frequency * t)\n",
    "    plt.plot(t, i_s, 'r-', label=\"I * cos(2 $\\pi$ f t)\")\n",
    "    plt.legend()\n",
    "    plt.xlabel('time')\n",
    "    plt.ylim(-3, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7102f906-3151-4f1a-87b4-5aa9fc07ad1f",
   "metadata": {},
   "source": [
    "To allow efficient experiments with the function above, the `interact` function allows calling the function repeatedly with the inputs being adjusted by UI controls. In our case, `I` can take any value between -2 and 2 in steps of 0.02. There won't be controls for the frequency or samples, since both are set to fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bffd4505-1ab3-45e6-bdea-67c98e6eb50a",
   "metadata": {},
   "outputs": [],
   "source": [
    "interact(iq_plot, I=(-2, 2, 0.02), frequency=fixed(0.2), samples=fixed(150))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a09f852-8bb0-42ca-a3af-327bccbc601a",
   "metadata": {},
   "source": [
    "It is your task to extend the `iq_plot` function to also plot the quadrature component and the sum of the two components. Give functions a proper label so they are easy to identify by the given legend. Also, name the y axis \"amplitude\".\n",
    "Finally, add a second slider to the `interact` output that allows to adjust the quadrature component as well."
   ]
  }
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