{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<img align=\"left\" style=\"padding-right:10px;\" src=\"images/book_cover.jpg\" width=\"120\">\n",
    "\n",
    "*This notebook contains an excerpt from the [Python Programming and Numerical Methods - A Guide for Engineers and Scientists](https://www.elsevier.com/books/python-programming-and-numerical-methods/kong/978-0-12-819549-9), the content is also available at [Berkeley Python Numerical Methods](https://pythonnumericalmethods.berkeley.edu/notebooks/Index.html).*\n",
    "\n",
    "*The copyright of the book belongs to Elsevier. We also have this interactive book online for a better learning experience. The code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work on [Elsevier](https://www.elsevier.com/books/python-programming-and-numerical-methods/kong/978-0-12-819549-9) or [Amazon](https://www.amazon.com/Python-Programming-Numerical-Methods-Scientists/dp/0128195495/ref=sr_1_1?dchild=1&keywords=Python+Programming+and+Numerical+Methods+-+A+Guide+for+Engineers+and+Scientists&qid=1604761352&sr=8-1)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [24.4 FFT in Python](chapter24.04-FFT-in-Python.ipynb) | [Contents](Index.ipynb) | [CHAPTER 25. Introduction to Machine Learning](chapter25.00-Introduction-to-Machine-Learning.ipynb)  >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
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   },
   "source": [
    "# Summary\n",
    "\n",
    "\n",
    "1. We learned the basics of the waves, frequency, period, amplitude and wavelength are the characteristics of the waves.\n",
    "2. The Discrete Fourier Transform (DFT) is a way to transform a signal from time domain to frequency domain using the sum of a sequence of sine waves. \n",
    "3. The Fast Fourier Transform (FFT) is an algorithm to calculate the DFTs efficiently by taking advantage of the symmetry properties in DFT. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Problems\n",
    "\n",
    "1. A task assigned to you to measure the temperature of the room. Thus everyday at noon, you measure the temperature and record the value. You measured for 30 days. What's the frequency of the temperature signal you get?\n",
    "2. What's the relationship of the frequency and period of a wave?\n",
    "3. What's the difference of period and wavelength? What are the similarities between them?\n",
    "4. What are the time domain and frequency domain representation of a signal?\n",
    "5. Generate two signals, signal 1 is a sine wave with 5 Hz, amplitude 3 and phase shift 3, signal 2 is a sine wave with 2 Hz, amplitude 2 and phase shift -2. Plot the signal for 2 seconds. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.style.use('seaborn-poster')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sampling rate\n",
    "sr = 100\n",
    "# sampling interval\n",
    "ts = 1.0/sr\n",
    "t = np.arange(0,2,ts)\n",
    "\n",
    "freq = 5.\n",
    "x = 3*np.sin(2*np.pi*freq*t + 3)\n",
    "\n",
    "freq = 2\n",
    "x += 2*np.sin(2*np.pi*freq*t - 2)\n",
    "\n",
    "\n",
    "plt.figure(figsize = (8, 6))\n",
    "plt.plot(t, x, 'r')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.xlabel('Time (s)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6. Sample the signal you generated in problem 5 using a sampling rate 5, 10, 20, 50, and 100 Hz, and see the differences between different sampling rates. \n",
    "7. Given a signal t = [0, 1, 2, 3], and y = [0, 3, 2, 0], find the real DFT of X. Write the expression for the inverse DFT. Note that, don't use Python to find the results, instead write out the equations and calculate the values. \n",
    "8. What are the amplitude and phase of the DFT values for a signal? \n",
    "9. We implement the DFT previously, can you implement the inverse Discrete Fourier Transform in Python similarly?\n",
    "10. Use the DFT function and inverse DFT we implemented and generate the amplitude spectrum for the signal you generated in problem 5. Normalize the DFT amplitude to get the correct corresponding time domain amplitude. \n",
    "11. Can you describe the tricks used in FFT to make the computation faster?\n",
    "12. Use the fft and ifft function from scipy to repeat problem 10. \n",
    "13. Adding a random normal distribution noise into the signal in problem 5 using numpy and plot the FFT amplitude spectrum, what do you see? The signal with noise will be shown as the following test case. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(10)\n",
    "x_noise = x + \\\n",
    "  np.random.normal(0, 2, size = len(x))\n",
    "\n",
    "plt.figure(figsize = (8, 6))\n",
    "plt.plot(t, x_noise, 'r')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.xlabel('Time (s)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [24.4 FFT in Python](chapter24.04-FFT-in-Python.ipynb) | [Contents](Index.ipynb) | [CHAPTER 25. Introduction to Machine Learning](chapter25.00-Introduction-to-Machine-Learning.ipynb)  >"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
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 },
 "nbformat": 4,
 "nbformat_minor": 2
}
