no commit message

parent 9b3d0eb4
...@@ -9,7 +9,7 @@ ...@@ -9,7 +9,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 508, "execution_count": 1,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -35,7 +35,7 @@ ...@@ -35,7 +35,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 509, "execution_count": 2,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -257,7 +257,7 @@ ...@@ -257,7 +257,7 @@
"[756 rows x 10 columns]" "[756 rows x 10 columns]"
] ]
}, },
"execution_count": 509, "execution_count": 2,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -289,7 +289,7 @@ ...@@ -289,7 +289,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 510, "execution_count": 3,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -310,7 +310,7 @@ ...@@ -310,7 +310,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 511, "execution_count": 4,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -425,7 +425,7 @@ ...@@ -425,7 +425,7 @@
"4 1958 5 21320 1958.3699 317.51 314.71 317.86 315.06 317.51 314.71" "4 1958 5 21320 1958.3699 317.51 314.71 317.86 315.06 317.51 314.71"
] ]
}, },
"execution_count": 511, "execution_count": 4,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -443,7 +443,7 @@ ...@@ -443,7 +443,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 512, "execution_count": 5,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -486,7 +486,7 @@ ...@@ -486,7 +486,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 513, "execution_count": 6,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -601,7 +601,7 @@ ...@@ -601,7 +601,7 @@
"75 1964 4 23482 1964.2896 NaN NaN 321.83 319.45 321.83 319.45" "75 1964 4 23482 1964.2896 NaN NaN 321.83 319.45 321.83 319.45"
] ]
}, },
"execution_count": 513, "execution_count": 6,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -612,7 +612,7 @@ ...@@ -612,7 +612,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 514, "execution_count": 7,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -727,7 +727,7 @@ ...@@ -727,7 +727,7 @@
"6 1958 7 21381 1958.5370 315.86 315.19 315.86 315.22 315.86 315.19" "6 1958 7 21381 1958.5370 315.86 315.19 315.86 315.22 315.86 315.19"
] ]
}, },
"execution_count": 514, "execution_count": 7,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -746,7 +746,7 @@ ...@@ -746,7 +746,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 515, "execution_count": 8,
"metadata": { "metadata": {
"scrolled": true "scrolled": true
}, },
...@@ -892,7 +892,7 @@ ...@@ -892,7 +892,7 @@
"1958-08-01 315.29 314.93 316.19 " "1958-08-01 315.29 314.93 316.19 "
] ]
}, },
"execution_count": 515, "execution_count": 8,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -918,7 +918,7 @@ ...@@ -918,7 +918,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 516, "execution_count": 9,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -949,7 +949,7 @@ ...@@ -949,7 +949,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 517, "execution_count": 10,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -1001,7 +1001,7 @@ ...@@ -1001,7 +1001,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 518, "execution_count": 11,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -1056,7 +1056,7 @@ ...@@ -1056,7 +1056,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 519, "execution_count": 12,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -1200,7 +1200,7 @@ ...@@ -1200,7 +1200,7 @@
"1964-04-01 321.83 319.45 " "1964-04-01 321.83 319.45 "
] ]
}, },
"execution_count": 519, "execution_count": 12,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -1216,7 +1216,7 @@ ...@@ -1216,7 +1216,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 520, "execution_count": 13,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -1360,7 +1360,7 @@ ...@@ -1360,7 +1360,7 @@
"2020-01-01 413.05 413.37 413.33 " "2020-01-01 413.05 413.37 413.33 "
] ]
}, },
"execution_count": 520, "execution_count": 13,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -1378,7 +1378,7 @@ ...@@ -1378,7 +1378,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 521, "execution_count": 14,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -1621,7 +1621,7 @@ ...@@ -1621,7 +1621,7 @@
"[743 rows x 11 columns]" "[743 rows x 11 columns]"
] ]
}, },
"execution_count": 521, "execution_count": 14,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -1633,7 +1633,7 @@ ...@@ -1633,7 +1633,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 522, "execution_count": 15,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -1876,7 +1876,7 @@ ...@@ -1876,7 +1876,7 @@
"[12 rows x 11 columns]" "[12 rows x 11 columns]"
] ]
}, },
"execution_count": 522, "execution_count": 15,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -1888,7 +1888,7 @@ ...@@ -1888,7 +1888,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 523, "execution_count": 16,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -1897,7 +1897,7 @@ ...@@ -1897,7 +1897,7 @@
"1.6731473990043244e-11" "1.6731473990043244e-11"
] ]
}, },
"execution_count": 523, "execution_count": 16,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -1926,7 +1926,7 @@ ...@@ -1926,7 +1926,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 524, "execution_count": 17,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -1935,7 +1935,7 @@ ...@@ -1935,7 +1935,7 @@
"<StemContainer object of 3 artists>" "<StemContainer object of 3 artists>"
] ]
}, },
"execution_count": 524, "execution_count": 17,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
}, },
...@@ -1979,7 +1979,7 @@ ...@@ -1979,7 +1979,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 532, "execution_count": 30,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -2002,7 +2002,7 @@ ...@@ -2002,7 +2002,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 588, "execution_count": 31,
"metadata": { "metadata": {
"scrolled": true "scrolled": true
}, },
...@@ -2027,17 +2027,17 @@ ...@@ -2027,17 +2027,17 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 589, "execution_count": 32,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"[<matplotlib.lines.Line2D at 0x7fef40322358>,\n", "[<matplotlib.lines.Line2D at 0x7f8e8cd32128>,\n",
" <matplotlib.lines.Line2D at 0x7fef40266f98>]" " <matplotlib.lines.Line2D at 0x7f8e8cd67f28>]"
] ]
}, },
"execution_count": 589, "execution_count": 32,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
}, },
...@@ -2060,24 +2060,147 @@ ...@@ -2060,24 +2060,147 @@
"plt.plot(x,yopt,x,s1)" "plt.plot(x,yopt,x,s1)"
] ]
}, },
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Il n'est pas possible d'obtenir la période de la fréquence lente, pour deux raisons : \n",
"- Pour la FFT le signal est trop court pour extraire une information lente\n",
"- Pour l'approximation avec une sinus, ce n'est pas possible car l'oscillation rapide à une forte amplitude"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nous allons filtrer le signal pas un filtre passe bas pour ne garder que la variation lente."
]
},
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 586, "execution_count": 57,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"0.0825" "[<matplotlib.lines.Line2D at 0x7f8e8bbd3978>]"
] ]
}, },
"execution_count": 586, "execution_count": 57,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1296x360 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
} }
], ],
"source": [ "source": [
"0.99/12\n" "from scipy import signal\n",
"\n",
"b, a = signal.butter(2, 0.03 ,analog=False)\n",
"w, h = signal.freqs(b, a)\n",
"\n",
"# Show that frequency response is the same\n",
"impulse = np.zeros(1000)\n",
"impulse[500] = 1\n",
"\n",
"# Applies filter forward and backward in time\n",
"imp_ff = signal.filtfilt(b, a, impulse)\n",
"\n",
"fig = plt.figure(figsize=(18, 5))\n",
"ax1 = fig.add_subplot(121)\n",
"ax2 = fig.add_subplot(122)\n",
"ax1.grid(linestyle='--', linewidth=1)\n",
"ax2.grid(linestyle='--', linewidth=1)\n",
"\n",
"#ax1.semilogx(w/(2*np.pi), 20 * np.log10(abs(h)))\n",
"ax1.semilogx(20*np.log10(np.abs(rfft(imp_ff))))\n",
"ax1.set(title = 'Reponse du filtre de Butterworth',xlabel='Fréquence [Hz]',ylabel='Amplitude [dB]')\n",
"#ax1.grid(which='both', axis='both')\n",
"\n",
"signal_filtrer = signal.filtfilt(b, a, s1)\n",
"#imp_lf = signal.lfilter(b, a, signal.lfilter(b, a, impulse))\n",
"ax2.plot(x,signal_filtrer)\n"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f8e8ece32e8>"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 3 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from numpy.random import randn\n",
"from numpy.fft import rfft\n",
"from scipy import signal\n",
"import matplotlib.pyplot as plt\n",
"\n",
"b, a = signal.butter(4, 0.03, analog=False)\n",
"\n",
"# Show that frequency response is the same\n",
"impulse = np.zeros(1000)\n",
"impulse[500] = 1\n",
"\n",
"# Applies filter forward and backward in time\n",
"imp_ff = signal.filtfilt(b, a, impulse)\n",
"\n",
"# Applies filter forward in time twice (for same frequency response)\n",
"imp_lf = signal.lfilter(b, a, signal.lfilter(b, a, impulse))\n",
"\n",
"plt.subplot(2, 2, 1)\n",
"plt.semilogx(20*np.log10(np.abs(rfft(imp_lf))))\n",
"plt.ylim(-100, 20)\n",
"plt.grid(True, which='both')\n",
"plt.title('lfilter')\n",
"\n",
"plt.subplot(2, 2, 2)\n",
"plt.semilogx(20*np.log10(np.abs(rfft(imp_ff))))\n",
"plt.ylim(-100, 20)\n",
"plt.grid(True, which='both')\n",
"plt.title('filtfilt')\n",
"\n",
"sig = np.cumsum(randn(800)) # Brownian noise\n",
"sig_ff = signal.filtfilt(b, a, sig)\n",
"sig_lf = signal.lfilter(b, a, signal.lfilter(b, a, sig))\n",
"plt.subplot(2, 1, 2)\n",
"plt.plot(sig, color='silver', label='Original')\n",
"plt.plot(sig_ff, color='#3465a4', label='filtfilt')\n",
"plt.plot(sig_lf, color='#cc0000', label='lfilter')\n",
"plt.grid(True, which='both')\n",
"plt.legend(loc=\"best\")"
] ]
}, },
{ {
......
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