Ajout des notebooks TD2 à TD8 + ajout des fichiers

# Historique
* [X] Ajout de requirements.txt pour gestion des dépendances
* [X] Ajout du fichier .py et du notebook jupyter .ipynb pour TD1
* [X] Création d'un git pour Stat

README.md

-Ajout de requirement.txt pour gestion des dépendances
+Ajout des notebooks TD2 à TD8 + ajout des fichiers
 # Historique
+* [X] Ajout de requirements.txt pour gestion des dépendances
 * [X] Ajout du fichier .py et du notebook jupyter .ipynb pour TD1
 * [X] Création d'un git pour Stat

TD2.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#!/usr/bin/python\n",
+    "# coding: utf-8\n",
+    "\n",
+    "#################################################\"    \n",
+    "##                 MODULES                  #####\"\n",
+    "#################################################\"\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "#################################################\"\n",
+    "\n",
+    "# Parameters\n",
+    "\n",
+    "N = 500                     # Number of sampling\n",
+    "Tmax = 2.0                  # Max time\n",
+    "Te = Tmax/N                  # Delta time between each measurements\n",
+    "f1=1                         # Acquisition frequency\n",
+    "t = np.arange(0, Tmax, Te)   # Time vector\n",
+    "\n",
+    "# Functions\n",
+    "u1=0.5*1.0*np.cos(2*np.pi*f1*t)\n",
+    "u2=0.3*np.cos(2*2*np.pi*f1*t-np.pi/3)\n",
+    "u=u1+u2\n",
+    "\n",
+    "# fft analysis\n",
+    "Puu=np.abs(np.fft.fft(u,N)/N)**2  # Density spectrum\n",
+    "freqs=np.linspace(0,1/Te,len(Puu)) # frequencies\n",
+    "\n",
+    "# Figure\n",
+    "fig1=plt.figure(figsize=(10,5))\n",
+    "plt.plot(freqs,Puu, 'ko-', label='u')\n",
+    "plt.axis([0,11,0,0.1])\n",
+    "plt.xlabel(\"Frequency (Hz)\")\n",
+    "plt.ylabel(\"Power spectrum\")\n",
+    "plt.grid()\n",
+    "plt.show()\n",
+    "\n",
+    "#   Save the figure\n",
+    "fig1.savefig('Figure_TD2',dpi=200)"
+   ]
+  }
+ ],
+ "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": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
+%% Cell type:code id: tags:
+
+``` python
+#!/usr/bin/python
+# coding: utf-8
+
+#################################################"
+##                 MODULES                  #####"
+#################################################"
+import matplotlib.pyplot as plt
+import numpy as np
+#################################################"
+
+# Parameters
+
+N = 500                     # Number of sampling
+Tmax = 2.0                  # Max time
+Te = Tmax/N                  # Delta time between each measurements
+f1=1                         # Acquisition frequency
+t = np.arange(0, Tmax, Te)   # Time vector
+
+# Functions
+u1=0.5*1.0*np.cos(2*np.pi*f1*t)
+u2=0.3*np.cos(2*2*np.pi*f1*t-np.pi/3)
+u=u1+u2
+
+# fft analysis
+Puu=np.abs(np.fft.fft(u,N)/N)**2  # Density spectrum
+freqs=np.linspace(0,1/Te,len(Puu)) # frequencies
+
+# Figure
+fig1=plt.figure(figsize=(10,5))
+plt.plot(freqs,Puu, 'ko-', label='u')
+plt.axis([0,11,0,0.1])
+plt.xlabel("Frequency (Hz)")
+plt.ylabel("Power spectrum")
+plt.grid()
+plt.show()
+
+#   Save the figure
+fig1.savefig('Figure_TD2',dpi=200)
+```

TD3.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#!/usr/bin/python\n",
+    "# coding: utf-8\n",
+    "\n",
+    "#################################################\"    \n",
+    "##                 MODULES                  #####\"\n",
+    "#################################################\"\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "#################################################\"\n",
+    "\n",
+    "# Parameters\n",
+    "N = 500                     # Number of sampling\n",
+    "Tmax = 2.0                  # Max time\n",
+    "Te = Tmax/N                  # Delta time between each measurements\n",
+    "f1=1                         # Acquisition frequency\n",
+    "t = np.arange(0, Tmax, Te)   # Time vector\n",
+    "\n",
+    "\n",
+    "# Functions\n",
+    "u1=2*1.0*np.cos(2*np.pi*f1*t)\n",
+    "u2=2*np.cos(2*2*np.pi*f1*t-np.pi/3)\n",
+    "u=u1+u2\n",
+    "\n",
+    "# Analyse statistique\n",
+    "nbrv=(np.diff(np.sign(u)) < 0).sum()# Nbr d'oscillations\n",
+    "hist, bin_edges = np.histogram(u, bins=20) #Fonction de repartition des hauteurs de vagues. \n",
+    "X = np.sort(u)\n",
+    "F = np.array(range(N))*100/float(N)\n",
+    "H13=np.mean(X[np.where(F>66)])      # Calcul de la moyenne du tiers superieur des oscillations\n",
+    "fu=np.where((np.diff(np.sign(u)) < 0))\n",
+    "Tm=np.mean(np.diff(fu))*Te    # Calcul de la periode moyenne\n",
+    "\n",
+    "\n",
+    "# Figure\n",
+    "fig1=plt.figure(figsize=(10,5))\n",
+    "plt.bar(bin_edges[:-1], hist, width=bin_edges[1]-bin_edges[0], color='red', alpha=0.5, label='Histogramm')\n",
+    "plt.plot(X, F, label=u'cumulative frequency')\n",
+    "plt.xlabel(\"oscillation amplitude\")\n",
+    "plt.ylabel(u\"Probability\")\n",
+    "titre='Amplitude histogram: H1/3=' + str(np.around(H13,2))+'; Tm='+str(np.around(Tm,2))\n",
+    "plt.title(titre)\n",
+    "plt.legend()\n",
+    "plt.grid()\n",
+    "plt.ylim(0,100)\n",
+    "plt.show()\n",
+    "\n",
+    "#   Save the figure\n",
+    "fig1.savefig('Figure_TD3',dpi=200)\n"
+   ]
+  }
+ ],
+ "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": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
+%% Cell type:code id: tags:
+
+``` python
+#!/usr/bin/python
+# coding: utf-8
+
+#################################################"
+##                 MODULES                  #####"
+#################################################"
+import matplotlib.pyplot as plt
+import numpy as np
+#################################################"
+
+# Parameters
+N = 500                     # Number of sampling
+Tmax = 2.0                  # Max time
+Te = Tmax/N                  # Delta time between each measurements
+f1=1                         # Acquisition frequency
+t = np.arange(0, Tmax, Te)   # Time vector
+
+
+# Functions
+u1=2*1.0*np.cos(2*np.pi*f1*t)
+u2=2*np.cos(2*2*np.pi*f1*t-np.pi/3)
+u=u1+u2
+
+# Analyse statistique
+nbrv=(np.diff(np.sign(u)) < 0).sum()# Nbr d'oscillations
+hist, bin_edges = np.histogram(u, bins=20) #Fonction de repartition des hauteurs de vagues.
+X = np.sort(u)
+F = np.array(range(N))*100/float(N)
+H13=np.mean(X[np.where(F>66)])      # Calcul de la moyenne du tiers superieur des oscillations
+fu=np.where((np.diff(np.sign(u)) < 0))
+Tm=np.mean(np.diff(fu))*Te    # Calcul de la periode moyenne
+
+
+# Figure
+fig1=plt.figure(figsize=(10,5))
+plt.bar(bin_edges[:-1], hist, width=bin_edges[1]-bin_edges[0], color='red', alpha=0.5, label='Histogramm')
+plt.plot(X, F, label=u'cumulative frequency')
+plt.xlabel("oscillation amplitude")
+plt.ylabel(u"Probability")
+titre='Amplitude histogram: H1/3=' + str(np.around(H13,2))+'; Tm='+str(np.around(Tm,2))
+plt.title(titre)
+plt.legend()
+plt.grid()
+plt.ylim(0,100)
+plt.show()
+
+#   Save the figure
+fig1.savefig('Figure_TD3',dpi=200)
+```

TD4.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#!/usr/bin/python\n",
+    "# coding: utf-8\n",
+    "\n",
+    "#################################################\"    \n",
+    "##                 MODULES                  #####\"\n",
+    "#################################################\"\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "#################################################\"\n",
+    "\n",
+    "# Parameters\n",
+    "N = 1000                     # Number of sampling\n",
+    "Tmax = 4.0                  # Max time\n",
+    "Te = Tmax/N                  # Delta time between each measurements\n",
+    "f1=1                       # Acquisition frequency (Hz)\n",
+    "t = np.arange(0, Tmax, Te)   # Time vector\n",
+    "\n",
+    "\n",
+    "\n",
+    "# Functions\n",
+    "u1=0.5*np.cos(1*2*np.pi*f1*t)\n",
+    "u2=0.3*np.cos(2*2*np.pi*f1*t-np.pi/3)\n",
+    "u=u1+u2\n",
+    "\n",
+    "# fft analysis\n",
+    "y=np.fft.rfft(u,N)/N      # Fast Fourier Transform\n",
+    "a0=2*y[0].real           # Fourier coeff a0\n",
+    "a=2*y.real        # Fourier coeff a\n",
+    "b=-2*y.imag         # Fourier coeff b\n",
+    "\n",
+    "# Rebuilding the harmonics\n",
+    "n=1                          # Number of harmonics\n",
+    "m=int(Tmax)*f1*n\n",
+    "v1=a[m]*np.cos(2*np.pi*f1*t)+b[m]*np.sin(2*np.pi*f1*t)\n",
+    "#\n",
+    "n=2                         # Number of harmonics\n",
+    "m=int(Tmax)*f1*n\n",
+    "v2=a[m]*np.cos(n*2*np.pi*f1*t)+b[m]*np.sin(n*2*np.pi*f1*t)\n",
+    "#\n",
+    "v=a0+v1+v2\n",
+    "\n",
+    "# Figure\n",
+    "fig1=plt.figure(figsize=(10,5))\n",
+    "#plt.hold(True)\n",
+    "plt.plot(t,u, 'r--', label='u')\n",
+    "plt.plot(t,u1, 'y--', label='u1')\n",
+    "plt.plot(t,u2, 'g--', label='u2')\n",
+    "plt.plot(t,v, 'ro', label='v')\n",
+    "plt.plot(t,v1, 'yo', label='v1')\n",
+    "plt.plot(t,v2, 'go', label='v2')\n",
+    "plt.legend()\n",
+    "plt.xlabel(\"t\")\n",
+    "plt.ylabel(\"f(t)\")\n",
+    "#plt.axis([0,2,-2,2])\n",
+    "plt.grid()\n",
+    "plt.show()\n",
+    "\n",
+    "#   Save the figure\n",
+    "fig1.savefig('Figure_TD3',dpi=200)\n",
+    "\n",
+    "\n"
+   ]
+  }
+ ],
+ "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": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
+%% Cell type:code id: tags:
+
+``` python
+#!/usr/bin/python
+# coding: utf-8
+
+#################################################"
+##                 MODULES                  #####"
+#################################################"
+import matplotlib.pyplot as plt
+import numpy as np
+#################################################"
+
+# Parameters
+N = 1000                     # Number of sampling
+Tmax = 4.0                  # Max time
+Te = Tmax/N                  # Delta time between each measurements
+f1=1                       # Acquisition frequency (Hz)
+t = np.arange(0, Tmax, Te)   # Time vector
+
+
+
+# Functions
+u1=0.5*np.cos(1*2*np.pi*f1*t)
+u2=0.3*np.cos(2*2*np.pi*f1*t-np.pi/3)
+u=u1+u2
+
+# fft analysis
+y=np.fft.rfft(u,N)/N      # Fast Fourier Transform
+a0=2*y[0].real           # Fourier coeff a0
+a=2*y.real        # Fourier coeff a
+b=-2*y.imag         # Fourier coeff b
+
+# Rebuilding the harmonics
+n=1                          # Number of harmonics
+m=int(Tmax)*f1*n
+v1=a[m]*np.cos(2*np.pi*f1*t)+b[m]*np.sin(2*np.pi*f1*t)
+#
+n=2                         # Number of harmonics
+m=int(Tmax)*f1*n
+v2=a[m]*np.cos(n*2*np.pi*f1*t)+b[m]*np.sin(n*2*np.pi*f1*t)
+#
+v=a0+v1+v2
+
+# Figure
+fig1=plt.figure(figsize=(10,5))
+#plt.hold(True)
+plt.plot(t,u, 'r--', label='u')
+plt.plot(t,u1, 'y--', label='u1')
+plt.plot(t,u2, 'g--', label='u2')
+plt.plot(t,v, 'ro', label='v')
+plt.plot(t,v1, 'yo', label='v1')
+plt.plot(t,v2, 'go', label='v2')
+plt.legend()
+plt.xlabel("t")
+plt.ylabel("f(t)")
+#plt.axis([0,2,-2,2])
+plt.grid()
+plt.show()
+
+#   Save the figure
+fig1.savefig('Figure_TD3',dpi=200)
+
+
+```

TD5.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#!/usr/bin/python\n",
+    "# coding: utf-8\n",
+    "\n",
+    "#################################################\"    \n",
+    "##                 MODULES                  #####\"\n",
+    "#################################################\"\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "#################################################\"\n",
+    "\n",
+    "\n",
+    "# Parameters\n",
+    "\n",
+    "N = 1000                     # Number of sampling\n",
+    "Tmax = 4.0                  # Max time\n",
+    "Te = Tmax/N                  # Delta time between each measurements\n",
+    "f1=1                 # Acquisition frequency (Hz)\n",
+    "t = np.arange(0, Tmax, Te)   # Time vector\n",
+    "n=4                          # Number of harmonics\n",
+    "\n",
+    "# Functions\n",
+    "\n",
+    "u1=0.5*np.cos(1*2*np.pi*f1*t)\n",
+    "u2=0.3*np.cos(2*2*np.pi*f1*t-np.pi/3)\n",
+    "u3=0.5*np.cos(3*2*np.pi*f1*t+np.pi/3)\n",
+    "u4=0.1*np.cos(4*2*np.pi*f1*t)\n",
+    "u=u1+u2+u3+u4\n",
+    "\n",
+    "# fft analysis\n",
+    "y=np.fft.fft(u)    #Fast Fourier Transform\n",
+    "\n",
+    "# order of the filtering\n",
+    "m=int(Tmax)*f1*n+1\n",
+    "\n",
+    "y[m:-m]=0\n",
+    "# Reverse fft and normalize\n",
+    "Y=np.fft.ifft(y)\n",
+    "Y=Y.real\n",
+    "\n",
+    "# Figure\n",
+    "fig1=plt.figure(figsize=(10,5))\n",
+    "plt.plot(t, Y, 'k.', label='filtered dataset')\n",
+    "plt.plot(t,u, 'r--', label=\"Original dataset\")\n",
+    "plt.legend()\n",
+    "plt.xlabel(\"t\")\n",
+    "plt.ylabel(\"u\")\n",
+    "plt.show()\n",
+    "\n",
+    "#   Save the figure\n",
+    "fig1.savefig('Figure_TD5',dpi=200)"
+   ]
+  }
+ ],
+ "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": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
+%% Cell type:code id: tags:
+
+``` python
+#!/usr/bin/python
+# coding: utf-8
+
+#################################################"
+##                 MODULES                  #####"
+#################################################"
+import matplotlib.pyplot as plt
+import numpy as np
+#################################################"
+
+
+# Parameters
+
+N = 1000                     # Number of sampling
+Tmax = 4.0                  # Max time
+Te = Tmax/N                  # Delta time between each measurements
+f1=1                 # Acquisition frequency (Hz)
+t = np.arange(0, Tmax, Te)   # Time vector
+n=4                          # Number of harmonics
+
+# Functions
+
+u1=0.5*np.cos(1*2*np.pi*f1*t)
+u2=0.3*np.cos(2*2*np.pi*f1*t-np.pi/3)
+u3=0.5*np.cos(3*2*np.pi*f1*t+np.pi/3)
+u4=0.1*np.cos(4*2*np.pi*f1*t)
+u=u1+u2+u3+u4
+
+# fft analysis
+y=np.fft.fft(u)    #Fast Fourier Transform
+
+# order of the filtering
+m=int(Tmax)*f1*n+1
+
+y[m:-m]=0
+# Reverse fft and normalize
+Y=np.fft.ifft(y)
+Y=Y.real
+
+# Figure
+fig1=plt.figure(figsize=(10,5))
+plt.plot(t, Y, 'k.', label='filtered dataset')
+plt.plot(t,u, 'r--', label="Original dataset")
+plt.legend()
+plt.xlabel("t")
+plt.ylabel("u")
+plt.show()
+
+#   Save the figure
+fig1.savefig('Figure_TD5',dpi=200)
+```

TD6.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#!/usr/bin/python\n",
+    "# coding: utf-8\n",
+    "\n",
+    "#################################################\"    \n",
+    "##                 MODULES                  #####\"\n",
+    "#################################################\"\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "#################################################\"\n",
+    "n=1   # Number of harmonics\n",
+    "\n",
+    "# Read ascii file\n",
+    "\n",
+    "filename='fichier2.txt'\n",
+    "with open(filename, 'r') as f:\n",
+    "    lines=f.readlines()\n",
+    "t=[]\n",
+    "u=[]\n",
+    "for l in lines:\n",
+    "    value=l.strip().split(\"\\t\")\n",
+    "    t.append(float(value[0]))           # Read the first column: time t\n",
+    "    u.append(float(value[1]))           # Read the second column: function u \n",
+    "\n",
+    "t=np.array(t)\n",
+    "u=np.array(u)\n",
+    "# Parameters\n",
+    "f1=1\n",
+    "N=len(t)\n",
+    "Tmax=np.round(max(t))\n",
+    "\n",
+    "# fft analysis\n",
+    "y=np.fft.fft(u)    #Fast Fourier Transform\n",
+    "\n",
+    "# order of the filtering\n",
+    "m=int(Tmax)*f1*n+1\n",
+    "y[m:-m]=0\n",
+    "# Reverse fft and normalize\n",
+    "Y=np.fft.ifft(y)\n",
+    "Y=Y.real\n",
+    "# Figure\n",
+    "fig1=plt.figure(figsize=(10,5))\n",
+    "plt.plot(t,u, 'r--', label=\"Original dataset\")\n",
+    "plt.plot(t, Y, 'k.', label='filtered dataset')\n",
+    "plt.legend()\n",
+    "plt.grid()\n",
+    "plt.show()\n",
+    "#   Save the figure\n",
+    "fig1.savefig('Figure_TD6',dpi=200)"
+   ]
+  }
+ ],
+ "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": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
+%% Cell type:code id: tags:
+
+``` python
+#!/usr/bin/python
+# coding: utf-8
+
+#################################################"
+##                 MODULES                  #####"
+#################################################"
+import matplotlib.pyplot as plt
+import numpy as np
+#################################################"
+n=1   # Number of harmonics
+
+# Read ascii file
+