{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Universidade Federal do Rio Grande do Sul (UFRGS)   \n",
    "Programa de Pós-Graduação em Engenharia Civil (PPGEC)   \n",
    "\n",
    "# PEC00025: Introduction to Vibration Theory\n",
    "\n",
    "\n",
    "### Class 07 - The Fourier Transform\n",
    "\n",
    "[1.   Introduction](#section_1)  \n",
    "[2.   Formal definition](#section_2)  \n",
    "[3.   Fourier transform of some basic functions](#section_3)  \n",
    "[3.1. Constant function](#section_31)  \n",
    "[3.2. Sine and cosine functions](#section_32)  \n",
    "[4.   Transformation of derivatives](#section_4)  \n",
    "[5.   Convolution and translation theorems](#section_5)  \n",
    "[6.   The Fast Fourier Transform (FFT)](#section_6)  \n",
    "[7.   The spectral density and the periodogram](#section_7)  \n",
    "[7.1. Definition](#section_71)  \n",
    "[7.2. Example with a white noise](#section_72)  \n",
    "[7.3. Example with an accelerometer signal](#section_73)  \n",
    "[8.   Assignment](#section_8)\n",
    "\n",
    "---\n",
    "_Prof. Marcelo M. Rocha, Dr.techn._ [(ORCID)](https://orcid.org/0000-0001-5640-1020)  \n",
    "_Porto Alegre, RS, Brazil_ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing Python modules required for this notebook\n",
    "# (this cell must be executed with \"shift+enter\" before any other Python cell)\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from   MRPy import MRPy\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Introduction <a name=\"section_1\"></a> \n",
    "\n",
    "To understand the _Fourier transform_ we can firstly recall the _Fourier series_ concept, \n",
    "according which any _periodic function_ with period $T$ can be expressed as a sum of \n",
    "sines and cosines:\n",
    "\n",
    "$$ f(t) =   a_0 + \\sum_{k = 1}^\\infty \n",
    "           {a_k \\, \\cos \\omega_k t + b_k \\, \\sin \\omega_k t}$$\n",
    "\n",
    "with $f(t) = f(t + T)$ and $\\omega_k = 2k\\pi/T$, where:\n",
    "\n",
    "\\begin{align*}\n",
    " a_0 &= \\frac{1}{T} \\int_{-T/2}^{T/2} f(t) \\; dt \\\\ \\\\\n",
    " a_k &= \\frac{2}{T} \\int_{-T/2}^{T/2} \\cos \\omega_k t \\; f(t) \\; dt \\\\ \\\\\n",
    " b_k &= \\frac{2}{T} \\int_{-T/2}^{T/2} \\sin \\omega_k t \\; f(t) \\; dt\n",
    "\\end{align*}\n",
    "\n",
    "with $k = 1, 2, \\dots\\ \\infty$.\n",
    "Recalling that sine and cosine functions have zero mean implies that the \n",
    "series coefficient $a_0$ represents the mean value of function $f(t)$.\n",
    "For example, it can be shown that the Fourier series expansion of a \n",
    "_zero mean square wave_ is:\n",
    "\n",
    "$$ f(t) =   \\frac{4}{\\pi} \\; \\sum_{k = 1, 3, 5...}^\\infty \n",
    "            \\frac{1}{k}   \\;  \\sin \\omega_{2k+1} t $$\n",
    "\n",
    "which can be verified with some few Python lines as follows.\n",
    "Firstly we define a zero mean square wave with periodicity $T = 1$s:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 1\n"
     ]
    }
   ],
   "source": [
    "print(9//2, 9%2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T  =  1           # function periodicity in seconds\n",
    "N  =  1000        # number of discretization points\n",
    "\n",
    "t  =  np.linspace(0, T, N)\n",
    "f1 =  np.zeros(N)\n",
    "\n",
    "f1[:N//2] = 2.0   # first half period is filled\n",
    "f1 =   f1 - 1.0   # f1 has zero mean and amplitude one\n",
    "\n",
    "plt.plot(t,f1)\n",
    "plt.grid(True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we reconstitutes this same function from Fourier series as given before, but limiting\n",
    "the infinite summation to only ```Nk``` terms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Nk =  51\n",
    "f2 =  np.zeros(N)\n",
    "\n",
    "for k in range(1, Nk+1, 2):\n",
    "    wk   =  2*k*np.pi/T\n",
    "    f2  +=  np.sin(wk*t)/k\n",
    "\n",
    "f2 *= 4/np.pi\n",
    "\n",
    "plt.figure(1, figsize=(8, 6), clear=True)\n",
    "plt.plot(t, f1, 'b', t, f2, 'r')\n",
    "\n",
    "plt.xlim( 0, T);  plt.xlabel('time (s)') \n",
    "plt.ylim(-2, 2);  plt.ylabel('f(t)') \n",
    "\n",
    "plt.grid(True) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The approximation accuracy can be explored by changing the value assigned to ```Nk``` in\n",
    "the calculation above. \n",
    "\n",
    "It must be emphasized that the series coefficients $a_k$ and $b_k$ hold information about\n",
    "how to _reconstitutes_ the original function $f(t)$, so they may be seen as _transformed_\n",
    "functions of variable $\\omega_k$ instead of variable $t$.\n",
    "We will come back later showing how to numerically estimate the Fourier coefficients \n",
    "for any periodic function.\n",
    "\n",
    "Once the Fourier series concept has been understood, the _Fourier transform_ is presented \n",
    "in the next section as a extension of the Fourier series concept for $T \\rightarrow \\infty$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Formal definition  <a name=\"section_2\"></a> \n",
    "\n",
    "The Fourier series expansion can also be expressed for any real or complex function $f(t)$\n",
    "by replacing the sine and cosine functions in the previous definition with the \n",
    "Euler's formula:\n",
    "\n",
    "$$ e^{i\\omega_k t} = \\cos \\omega_k t + i \\sin \\omega_k t$$\n",
    "\n",
    "what gives:\n",
    "\n",
    "$$ f(t) =  \\sum_{k = -\\infty}^\\infty {F_k \\, e^{i \\omega_k t}} $$\n",
    "\n",
    "where:\n",
    "\n",
    "$$ F_k = \\frac{1}{T} \\int_{-T/2}^{T/2} {e^{-i \\omega_k t}} \\; f(t) \\; dt $$\n",
    "\n",
    "with $ k = 0, \\pm 1, \\pm 2, \\dots\\, \\pm \\infty$.\n",
    "\n",
    "Now the function periodicity is allowed to increase to infinite to yield the following limits:\n",
    "\n",
    "\\begin{align*}\n",
    "                               T  &\\rightarrow   \\infty    \\\\\n",
    "      \\omega_k = k \\Delta \\omega  &\\rightarrow   \\omega    \\\\\n",
    "          \\Delta \\omega = 2\\pi/T  &\\rightarrow  d\\omega\n",
    "\\end{align*}\n",
    "\n",
    "and also the definition:\n",
    "\n",
    "$$ \\lim_{T \\rightarrow \\infty} \\; \\left( T \\; F_k  \\right)\n",
    " = \\lim_{\\Delta \\omega \\rightarrow 0} \\; \\left( \\frac{2 \\pi} {\\Delta \\omega} \\; F_k \\right)\n",
    " = F(\\omega)$$\n",
    "\n",
    "which replaced on the series expansion for $f(t)$ gives:\n",
    "\n",
    "$$ f(t) = \\lim_{\\Delta \\omega \\rightarrow 0} \\; \n",
    "          \\left[ \\frac{1}{2 \\pi} \\sum_{k = -\\infty}^\\infty  e^{i \\omega_k t} \n",
    "          \\left( \\frac{2 \\pi}{\\Delta \\omega} \\; F_k  \\right)\n",
    "          \\Delta \\omega \\right] $$\n",
    "\n",
    "and hence:\n",
    "\n",
    "$$ f(t) = \\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty} {e^{i\\omega t}\\; F(\\omega) \\; d\\omega}\n",
    "        = \\mathscr{F}^{-1} \\left\\{ F(\\omega) \\right\\} $$\n",
    "\n",
    "with:\n",
    "\n",
    "$$ F(\\omega) = \\int_{-\\infty}^{\\infty} e^{-i\\omega t}\\; f(t) \\; dt \n",
    "             = \\mathscr{F}\\left\\{ f(t) \\right\\} $$\n",
    "\n",
    "which are the inverse and the direct _Fourier Transform_ definitions, respectively.\n",
    "Observing that both integral bounds are infinite, the function $f(t)$ \n",
    "must fulfill some special conditions such that the integral convergence\n",
    "can be ensured.\n",
    "The most important condition is that the integral of $\\left| f(t) \\right|$ \n",
    "over the complete domain exists:\n",
    "\n",
    "$$ \\exists \\int_{-\\infty}^{\\infty} \\left| f(\\xi) \\right| \\; d\\xi \\in {\\mathbb C}$$\n",
    "\n",
    "although in some special cases the transformation is possible even if this \n",
    "condition is not fulfilled.\n",
    "\n",
    "The transform of a given function and its inverse constitutes a so-called\n",
    "_transform pair_, usually represented as:\n",
    "\n",
    "$$ f(t) \\Longleftrightarrow F(\\omega) $$\n",
    "\n",
    "While the use of Laplace transforms mostly rely upon _lookup tables_ or CAS \n",
    "(_Computer Algebra Systems_), the Fourier transform, both direct and inverse, \n",
    "is usually evaluated by means of numerical techniques. \n",
    "Nevertheless, some fundamental functions and theorems must receive special \n",
    "attention as follows.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Fourier transform of some basic functions <a name=\"section_3\"></a> \n",
    "\n",
    "### 3.1. Constant function <a name=\"section_31\"></a> \n",
    "\n",
    "The constant function, $f(t) = c$, does not fulfill the condition for the transform existence\n",
    "(its integral over the whole domain is infinite), but by assuming that the inverse\n",
    "transform exists:\n",
    "\n",
    "$$ c  = \\frac{1}{2 \\pi} \\int_{-\\infty}^{\\infty} e^{i\\omega t}\\; F(\\omega) \\; d\\omega $$\n",
    "\n",
    "it can be observed that the only function satifying the integral is the Dirac's Delta:\n",
    "\n",
    "$$ F(\\omega) = 2\\pi c \\; \\delta(\\omega) $$\n",
    "\n",
    "Recalling that the Fourier transform is a linear operator, the function $f(t)$ can be\n",
    "decomposed as its mean value superposed to a fluctuation:\n",
    "\n",
    "$$f(t) = \\bar{f} + \\tilde{f}(t) $$\n",
    "\n",
    "This implies that, whenever the function has a non-zero mean value, its\n",
    "Fourier transform will also present an impulse function at the origin, $\\omega = 0$.\n",
    "We will numerically demonstrate this result later on.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2. Sine and cosine functions <a name=\"section_32\"></a> \n",
    "\n",
    "The trigonometric functions $\\sin(\\omega_0 t)$ and $\\cos(\\omega_0 t)$ also do not fulfill\n",
    "the condition for transform existence but, in the same way as for the constant function,\n",
    "a meaningful transform can be found. \n",
    "Observe that a given $\\omega_0$ is being used instead of the independent variable $\\omega$.\n",
    "\n",
    "Let us assume that the inverse transform of the Euler's formula exists:\n",
    "\n",
    "$$ f(t) = e^{i\\omega_0 t} = \\frac{1}{2 \\pi} \n",
    "          \\int_{-\\infty}^{\\infty} e^{i\\omega t}\\; F(\\omega) \\; d\\omega $$\n",
    "\n",
    "then again the only function satisfying this integral is the Dirac's Delta at $\\omega_0$.\n",
    "\n",
    "$$ F(\\omega) = 2 \\pi \\; \\delta (\\omega - \\omega_0)$$\n",
    "\n",
    "By going back from Euler's formula it can be easily demonstrated that for the cosine function\n",
    "it gives:\n",
    "\n",
    "$$ \\mathscr{F} \\left\\{ \\cos (\\omega_0 t) \\right\\} = \n",
    "   \\pi \\left[ \\delta(\\omega + \\omega_0) + \\delta(\\omega - \\omega_0) \\right]$$\n",
    "\n",
    "and similarly for the sine function:\n",
    "\n",
    "$$ \\mathscr{F} \\left\\{ \\sin (\\omega_0 t) \\right\\} = \n",
    "   i\\pi \\left[ \\delta(\\omega + \\omega_0) - \\delta(\\omega - \\omega_0) \\right]$$\n",
    "\n",
    "These two transforms are depicted below.\n",
    "\n",
    "<img src=\"images/Fourier_sine_cosine.png\" alt=\"Heaviside\" width=\"720px\"/>\n",
    "\n",
    "It can be seen that the cosine transform converges to the constant function transform\n",
    "as the frequency $\\omega_0$ goes to zero.\n",
    "These results will also be demonstrated after we introduce the numerical approach\n",
    "to the Fourier transform.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Transformation of derivatives <a name=\"section_4\"></a> \n",
    "\n",
    "The transformation of derivatives is essential for using Fourier transform \n",
    "for solving differential equations.\n",
    "The transform of a derivative is expressed as:\n",
    "\n",
    "$$ \\mathscr{F} \\left\\{ \\dot{f}(t) \\right\\} = \n",
    "   \\int_{-\\infty}^{\\infty} e^{-i\\omega t} \\; \\dot{f}(t) \\; dt $$\n",
    "\n",
    "This can be solved through integration by parts by defining:\n",
    "\n",
    "\\begin{array}{ll}\n",
    "   u  &= e^{-i\\omega t}              \\hspace{2cm}  &dv = \\dot{f}(t) \\; dt \\\\\n",
    "   du &= -i\\omega e^{-i\\omega t} dt                &v  = f(t)         \n",
    "\\end{array}\n",
    "\n",
    "and replacing in:\n",
    "\n",
    "$$ \\int u \\; dv = uv - \\int v \\; du$$\n",
    "\n",
    "Assuming that the function $f(t)$ may be zero at the far ends of the integration domain\n",
    "implies that the product $uv$ may be considered to vanish and hence:\n",
    "\n",
    "$$ \\int_{-\\infty}^{\\infty} e^{-i\\omega t} \\; \\dot{f}(t) \\; dt = \n",
    "   0 + i\\omega \\int_{-\\infty}^{\\infty} e^{-i\\omega t} \\; f(t) \\; dt$$\n",
    "\n",
    "and hence:\n",
    "\n",
    "$$ \\mathscr{F} \\left\\{ \\dot{f}(t) \\right\\} = i\\omega F(\\omega)$$\n",
    "\n",
    "For solving the dynamic equilibrium equation of linear systems, the second time\n",
    "derivative of $f(t)$ will also be necessary.\n",
    "Applying again the derivation rule results:\n",
    "\n",
    "$$ \\mathscr{F} \\left\\{ \\ddot{f}(t) \\right\\} = -\\omega^2 F(\\omega) $$\n",
    "\n",
    "Time derivatives of higher order can be calculated but will not be necessary in the\n",
    "present context.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. The convolution and translation theorems <a name=\"section_5\"></a> \n",
    "\n",
    "The convolution and translation theorems previously presented for Laplace transform\n",
    "also apply to the Fourier transform.\n",
    "The convolution reads:\n",
    "\n",
    "$$ \\mathscr{F} \\left\\{ f(t) * h(t) \\right\\} = F(\\omega) \\; H(\\omega) $$\n",
    "\n",
    "with:\n",
    "\n",
    "$$ f(t) * h(t) = \\int_{-\\infty}^{\\infty} {h(t - \\tau}) f(\\tau) \\,  \\; d\\tau$$\n",
    "\n",
    "where we are intentionally changing the notation from $\\bar{g}(s)$ and $g(t)$ \n",
    "(the unit impulse response function in Laplace Transform theory previously presented) \n",
    "to $H(\\omega)$ and $h(t)$, which will get a particular meaning in the frequency domain \n",
    "analysis with Fourier Transform.\n",
    "\n",
    "As for the Laplace Transform, the translation in frequency and time domain reads:\n",
    "\n",
    "$$ \\mathscr{F} \\left\\{ e^{\\omega_0 t} f(t) \\right\\} =  F(\\omega - \\omega_0) $$\n",
    "\n",
    "$$ \\mathscr{F} \\left\\{ f(t - \\tau) \\right\\} =  e^{-\\omega \\tau} \\; F(\\omega) $$\n",
    "\n",
    "These theorems will be of little use in this course.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. The Fast Fourier Transform (FFT) <a name=\"section_6\"></a> \n",
    "\n",
    "While there is no explicit form for the inverse Laplace transform, it was shown above that\n",
    "the same does not happen for the Fourier transform.\n",
    "This means that it can be numerically evaluated in both ways by means of a time and \n",
    "frequency domains discretization:\n",
    "\n",
    "\\begin{align*}\n",
    "\\omega_k &= k \\left( \\frac{2\\pi}{T} \\right), \\;\\;\\; k = 0, 1, 2, \\dots, N-1  \\\\ \\\\\n",
    "     t_j &= j \\left( \\frac{T}{N} \\right),    \\;\\;\\; j = 0, 1, 2, \\dots, N-1  \n",
    "\\end{align*}\n",
    "\n",
    "where $N$ is the length of a time series $f_j = f(t_j)$ with total duration $T$.\n",
    "The numerical calculation of the direct and inverse transforms are then:\n",
    "\n",
    "\\begin{align*}\n",
    "F_k &=             \\sum_{j=0}^{N-1} {f_j \\; \\exp\\left(-i\\omega_k t_j \\right)} \\\\ \\\\\n",
    "f_j &= \\frac{1}{N} \\sum_{k=0}^{N-1} {F_k \\; \\exp\\left( i\\omega_k t_j \\right)}\n",
    "\\end{align*}\n",
    "\n",
    "Observe that all the computation above requires $N^2$ evaluations of the \n",
    "trigonometric function $\\exp\\left(i 2\\pi k j \\right / N)$. \n",
    "Recognizing that the multiple permutations of indices $k$ and $i$ could be \n",
    "accounted to save computational time inspired the famous FFT algorithm by\n",
    "[Cooley and Tukey](https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm),\n",
    "which may reduce the number of exponential function evaluations up to $2N$.\n",
    "This algorithm is now implemented in many digital signal processing programs\n",
    "and is also available in the ```numpy``` and ```scipy``` modules in Python.\n",
    "\n",
    "For example, let us calculate the FFT of a constant function, as presented earlier:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "[8. 0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "[1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "[0. 0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "N  = 8                    # length of time series\n",
    "f1 = np.ones(N)           # assigning constant value 1\n",
    "F  = np.fft.fft(f1)       # calling FFT numpy function from fft submodule\n",
    "f2 = np.fft.ifft(F)       # inverse transform\n",
    "\n",
    "np.set_printoptions(precision=3)\n",
    "\n",
    "print(f1)\n",
    "print(F.real)\n",
    "print(F.imag)\n",
    "print(f2.real)\n",
    "print(f2.imag)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "what shows that the result is a real impulse function (discrete Dirac's Delta) at the origin.\n",
    "\n",
    "Let us now take a look at the cosine function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T  = 1                   # series total duration\n",
    "N  = 256                 # length of time series\n",
    "f0 = 2                   # sine/cosine frequency (in Hertz)\n",
    "\n",
    "k  = np.arange(0, N+1)   # required for f_k calculation\n",
    "ti = k*T/N               # discrete time domain\n",
    "fk = k/T                 # discrete frequency domain\n",
    "\n",
    "ci = np.cos(2*np.pi*f0*ti) + 1\n",
    "Ck = np.fft.fft(ci)\n",
    "\n",
    "plt.figure(2, figsize=(8, 4), clear=True)\n",
    "plt.plot(ti, ci)\n",
    "plt.xlim( 0, T);  plt.xlabel('time (s)') \n",
    "plt.ylim(-2, 2);  plt.ylabel('f(t)') \n",
    "plt.grid(True) \n",
    "\n",
    "plt.figure(3, figsize=(8, 6), clear=True)\n",
    "\n",
    "plt.subplot(2,1,1)\n",
    "plt.plot(fk, Ck.real)\n",
    "plt.xlim( 0, N/T);  plt.xlabel('frequency (Hz)')\n",
    "plt.ylim(-N, N  );  plt.ylabel('Real(F_k)') \n",
    "plt.grid(True) \n",
    "\n",
    "plt.subplot(2,1,2)\n",
    "plt.plot(fk, Ck.imag)\n",
    "plt.xlim( 0, N/T);  plt.xlabel('frequency (Hz)')\n",
    "plt.ylim(-N, N  );  plt.ylabel('Imag(F_k)') \n",
    "plt.grid(True) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The imaginary part of the result above, which refers to the sine transform,\n",
    "is a numerical error caused by the coarse representation of the cosine function.\n",
    "Try increasing the discretization (larger ```N```) and observe what happens.\n",
    "\n",
    "There are some few important issues to better understand the numerical result above:\n",
    "\n",
    "1. To get maximum algorithm efficiency, the length $N$ must be a power of 2.\n",
    "2. The value of $F_k$ for $k = 0$ is zero if $f(t)$ has zero mean (see [constant \n",
    "   function](#section_31) above).\n",
    "3. Since there is no negative time in the numerical transform, the algorithm returns \n",
    "   a vector $F_k$ such that its second half is the complex conjugate of the first half.\n",
    "   This means that the absolute value of $F_k$ is mirrowed at $k = N/2 + 1$.\n",
    "4. Although the Fourier transform is an extension of the Fourier series concept for\n",
    "   infinite periodicity, it is very important to keep in mind that the algorithm does\n",
    "   regard $f_i$ as periodic of length $N$. This can be demonstrated by changing the\n",
    "   previous example such that the cosine discretization does not respect the due\n",
    "   cosine periodicity (for instance, set the frequency to 1.5Hz instead of 2Hz).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. The spectral density and the periodogram <a name=\"section_7\"></a>\n",
    "\n",
    "### 7.1. Definition <a name=\"section_71\"></a>\n",
    "\n",
    "Given an undamped oscillator with mass $m$ and stifness $k = m\\omega^2$, \n",
    "subjected to force $F(t)$. The dynamic equilibrium equation is:\n",
    "\n",
    "$$ \\ddot{u} + \\omega^2 u = F(t)/m = f(t) $$\n",
    "\n",
    "Its internal energy, $w(t)$, is given at any moment by the sum of kinectic and \n",
    "elastic energies as:\n",
    "\n",
    "$$ w(t) = \\frac{1}{2} m \\left[ \\, \\dot{u}^2 + \\omega^2 u^2 \\, \\right]$$\n",
    "\n",
    "Recalling now the system solution with the convolution integral:\n",
    "\n",
    "$$ u(t) = \\frac{1}{\\omega} \\int_{-\\infty}^{\\infty} { f(\\tau) \\; \n",
    "          \\sin \\omega_{\\rm n}(t - \\tau) \\; d\\tau}$$\n",
    "\n",
    "and calculating its time derivative with the Leibnitz' rule:\n",
    "\n",
    "$$ \\dot{u}(t) = \\int_{-\\infty}^{\\infty} { f(\\tau) \\; \\cos \\omega(t - \\tau) \\; d\\tau}$$\n",
    "\n",
    "gives that:\n",
    "\n",
    "$$ w(t) = \\frac{1}{2} m \\left\\{\n",
    "          \\left[ \\, \\int_{-\\infty}^{\\infty} { f(\\tau) \\; \\cos \\omega(t - \\tau) \\; d\\tau} \\right]^2\n",
    "        + \\left[ \\, \\int_{-\\infty}^{\\infty} { f(\\tau) \\; \\sin \\omega(t - \\tau) \\; d\\tau} \\right]^2 \n",
    "          \\right\\}  $$ \n",
    "\n",
    "Applying the suitable trigonometric relations to $\\cos \\omega(t - \\tau)$ and \n",
    "$\\sin \\omega(t - \\tau)$ and doing some algebraic work leads to:\n",
    "\n",
    "$$ w(t)   \\propto \n",
    "          \\left[ \\, \\int_{-\\infty}^{\\infty} { f(\\tau) \\; \\cos \\omega\\tau \\; d\\tau} \\right]^2\n",
    "        + \\left[ \\, \\int_{-\\infty}^{\\infty} { f(\\tau) \\; \\sin \\omega\\tau \\; d\\tau} \\right]^2 $$ \n",
    "\n",
    "By recalling Euler's formula it can be recognized that the right hand side is the \n",
    "squared absolute value for the inverse Fourier transform of $F(\\omega)$, what means that \n",
    "$\\left| F(\\omega) \\right|^2$ is a measure of energy for a physical system subjected to \n",
    "excitation $f(t)$.\n",
    "We call it the _Power Spectral Density_ of $f(t)$, $S_F(\\omega)$:\n",
    "\n",
    "$$ S_F(\\omega) \\propto \\left| F(\\omega) \\right|^2$$\n",
    "\n",
    "The missing proportion constant is chosen such that the total area under the spectral density\n",
    "for $\\omega > 0$ matches the variance (squared standard deviation) $\\sigma_F^2$ of $f(t)$:\n",
    "\n",
    "$$ \\int_0^{\\infty} S_F(\\omega) \\; d\\omega = \\sigma_F^2$$\n",
    "\n",
    "Whenever a time series $f_i$ with length $N$ is available, there are many statistical \n",
    "estimators for $S_F(\\omega)$. \n",
    "The most basic of such estimators is the _periodogram_, directly calculate with the series\n",
    "FFT.\n",
    "This estimator is available in the ```MRPy``` module as a class method.\n",
    "\n",
    "\n",
    "### 7.2. Example with a white noise <a name=\"section_72\"></a>\n",
    "\n",
    "The following example shows how use the ``MRPy`` module to simulate a (almost) perfect white \n",
    "noise, and to how visualize the simulated signal both in time and frequency domain using\n",
    "the quick visualization methods.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.03125 0.9994923006355834\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X  = MRPy.white_noise(1, 1024, Td=8)                          # white noise simulation\n",
    "#X = MRPy(np.random.normal(0, 1, 1024), Td=8)\n",
    "\n",
    "print(X.mean(), X.std())\n",
    "\n",
    "f1 = X.plot_time(1, figsize=(8,3), axis_t=(0,  8, -3, 3   ))  # plot in time domain\n",
    "f2 = X.plot_freq(2, figsize=(8,3), axis_f=(0, 64,  0, 0.02))  # plot in frequency domain\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9993700392857929\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "SX, fs = X.periodogram()\n",
    "f      = X.f_axis()\n",
    "\n",
    "plt.figure(10)\n",
    "plt.plot(f, SX[0]);\n",
    "plt.grid(True)\n",
    "\n",
    "sX2 = np.trapz(SX[0], f)\n",
    "\n",
    "print(np.sqrt(sX2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.3. Example with an accelerometer signal <a name=\"section_73\"></a>\n",
    "\n",
    "This additional example shows how use the ``MRPy`` module to read a file with some\n",
    "acquired accelerometer signal, and how to visualize the read signal both in time and frequency domain\n",
    "using manually formatted plots.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Frequency at spectrum peak:  8.30Hz\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Reads csv file with accelerometer signal and isolates component a_z\n",
    "\n",
    "data = MRPy.from_file('resources/data/iNVH001', form='invh').zero_mean()\n",
    "az   = MRPy(data[2], data.fs)#extract((2.5,5), by='time')\n",
    "t    = az.t_axis()\n",
    "\n",
    "plt.figure(4, figsize=(8, 3), clear=True)\n",
    "plt.plot(t, az[0], lw=0.5)\n",
    "\n",
    "plt.xlim(0, az.Td);  plt.xlabel('time (s)') \n",
    "plt.ylim(-15, 15);   plt.ylabel('a_z (m/s^2)') \n",
    "\n",
    "plt.grid(True) \n",
    "\n",
    "# Calls method for periodogram calculation and visualize\n",
    "\n",
    "Saz, fs = az.periodogram()\n",
    "f       = az.f_axis()\n",
    "\n",
    "plt.figure(5, figsize=(8, 3), clear=True)\n",
    "plt.plot(f, Saz[0], lw=0.5)\n",
    "\n",
    "plt.xlim(0, 20);   plt.xlabel('frequency (Hz)') \n",
    "plt.ylim(0,  5);   plt.ylabel('S_az (power)') \n",
    "\n",
    "plt.grid(True) \n",
    "\n",
    "# Search for frequency associated to peak of spectrum\n",
    "\n",
    "kf = Saz[0].argmax()\n",
    "print('Frequency at spectrum peak: {0:5.2f}Hz'.format(f[kf]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plots above it may be concluded that the accelerometer signal has a strong\n",
    "energy density around 8Hz, what may indicate that the mechanical system presents a\n",
    "natural vibration frequency close to this value.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. Assignments <a name=\"section_8\"></a> \n",
    "\n",
    "1. Utilizar o mesmo registro de celular dos trabalhos anteriores.\n",
    "2. Importar os dados para a ```MRPy``` e apresentar os periodogramas\n",
    "   (estimativas das densidades espectrais), verificando qual a frequência\n",
    "   natural de vibração livre do objeto instrumentado pelo pico do gráfico.\n",
    "4. Relatório com descrição do objeto, gráficos e resultados (nome do arquivo            T5_xxxxxxxx.ipynb).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}