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Add chapter 10 code
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‎chapter10_signal/01_fourier.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Analyzing the frequency components of a signal with a Fast Fourier Transform"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import datetime\n",
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"import numpy as np\n",
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"import scipy as sp\n",
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"import scipy.fftpack\n",
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"import pandas as pd\n",
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"import matplotlib.pyplot as plt\n",
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"df0 = pd.read_csv('https://github.com/ipython-books/'\n",
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" 'cookbook-2nd-data/blob/master/'\n",
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" 'weather.csv?raw=true',\n",
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" na_values=(-9999),\n",
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" parse_dates=['DATE'])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"df = df0[df0['DATE'] >= '19940101']"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"df.head()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"df_avg = df.dropna().groupby('DATE').mean()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"df_avg.head()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"date = df_avg.index.to_datetime()\n",
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"temp = (df_avg['TMAX'] + df_avg['TMIN']) / 20.\n",
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"N = len(temp)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig, ax = plt.subplots(1, 1, figsize=(6, 3))\n",
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"temp.plot(ax=ax, lw=.5)\n",
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"ax.set_ylim(-10, 40)\n",
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"ax.set_xlabel('Date')\n",
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"ax.set_ylabel('Mean temperature')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"temp_fft = sp.fftpack.fft(temp)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"temp_psd = np.abs(temp_fft) ** 2"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [],
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"source": [
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"fftfreq = sp.fftpack.fftfreq(len(temp_psd), 1. / 365)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [],
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"source": [
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"i = fftfreq > 0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig, ax = plt.subplots(1, 1, figsize=(8, 4))\n",
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"ax.plot(fftfreq[i], 10 * np.log10(temp_psd[i]))\n",
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"ax.set_xlim(0, 5)\n",
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"ax.set_xlabel('Frequency (1/year)')\n",
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"ax.set_ylabel('PSD (dB)')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [],
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"source": [
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"temp_fft_bis = temp_fft.copy()\n",
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"temp_fft_bis[np.abs(fftfreq) > 1.1] = 0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [],
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"source": [
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"temp_slow = np.real(sp.fftpack.ifft(temp_fft_bis))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig, ax = plt.subplots(1, 1, figsize=(6, 3))\n",
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"temp.plot(ax=ax, lw=.5)\n",
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"ax.plot_date(date, temp_slow, '-')\n",
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"ax.set_xlim(datetime.date(1994, 1, 1),\n",
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" datetime.date(2000, 1, 1))\n",
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"ax.set_ylim(-10, 40)\n",
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"ax.set_xlabel('Date')\n",
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"ax.set_ylabel('Mean temperature')"
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]
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}
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],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎chapter10_signal/02_filter.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Applying a linear filter to a digital signal"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import scipy as sp\n",
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"import scipy.signal as sg\n",
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"import pandas as pd\n",
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"import matplotlib.pyplot as plt\n",
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"nasdaq_df = pd.read_csv(\n",
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" 'https://github.com/ipython-books/'\n",
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" 'cookbook-2nd-data/blob/master/'\n",
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" 'nasdaq.csv?raw=true', \n",
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" index_col='Date',\n",
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" parse_dates=['Date'])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"nasdaq_df.head()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"date = nasdaq_df.index\n",
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"nasdaq = nasdaq_df['Close']"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n",
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"nasdaq.plot(ax=ax, lw=1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"# We get a triangular window with 60 samples.\n",
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"h = sg.get_window('triang', 60)\n",
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"# We convolve the signal with this window.\n",
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"fil = sg.convolve(nasdaq, h / h.sum())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n",
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"# We plot the original signal...\n",
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"nasdaq.plot(ax=ax, lw=3)\n",
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"# ... and the filtered signal.\n",
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"ax.plot_date(date, fil[:len(nasdaq)],\n",
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" '-w', lw=2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n",
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"nasdaq.plot(ax=ax, lw=3)\n",
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"# We create a 4-th order Butterworth low-pass filter.\n",
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"b, a = sg.butter(4, 2. / 365)\n",
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"# We apply this filter to the signal.\n",
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"ax.plot_date(date, sg.filtfilt(b, a, nasdaq),\n",
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" '-w', lw=2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n",
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"nasdaq.plot(ax=ax, lw=1)\n",
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"b, a = sg.butter(4, 2 * 5. / 365, btype='high')\n",
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"ax.plot_date(date, sg.filtfilt(b, a, nasdaq),\n",
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" '-', lw=1)"
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]
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}
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],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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