Notebook

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Imports¶

The tutorial below imports NumPy, Pandas, SciPy and Plotly.

In [1]:

import plotly.plotly as py
import plotly.graph_objs as go
import plotly.figure_factory as ff

import numpy as np
import pandas as pd
import scipy

from scipy import signal

Import Data¶

Let us import some stock data to apply convolution on.

In [2]:

stock_data = pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/stockdata.csv')
df = stock_data[0:15]

table = ff.create_table(df)
py.iplot(table, filename='stockdata-peak-fitting')

Out[2]:

Convolve Two Signals¶

Convolution is a type of transform that takes two functions f and g and produces another function via an integration. In particular, the convolution $(f*g)(t)$ is defined as:

$$ \begin{align*} \int_{-\infty}^{\infty} {f(\tau)g(t - \tau)d\tau} \end{align*} $$

We can use convolution in the discrete case between two n-dimensional arrays.

In [11]:

sample = range(15)
saw = signal.sawtooth(t=sample)

data_sample = list(stock_data['SBUX'][0:100])
data_sample2 = list(stock_data['AAPL'][0:100])
x = list(range(len(data_sample)))
y_convolve = signal.convolve(saw, data_sample2)
x_convolve = list(range(len(y_convolve)))

trace1 = go.Scatter(
    x = x,
    y = data_sample,
    mode = 'lines',
    name = 'SBUX'
)

trace2 = go.Scatter(
    x = x,
    y = data_sample2,
    mode = 'lines',
    name = 'AAPL'
)

trace3 = go.Scatter(
    x = x_convolve,
    y = y_convolve,
    mode = 'lines',
    name = 'Convolution'
)

data = [trace1, trace2, trace3]
py.iplot(data, filename='convolution-of-two-signals')

Out[11]:

In [1]:

from IPython.display import display, HTML

display(HTML('<link href="//fonts.googleapis.com/css?family=Open+Sans:600,400,300,200|Inconsolata|Ubuntu+Mono:400,700" rel="stylesheet" type="text/css" />'))
display(HTML('<link rel="stylesheet" type="text/css" href="http://help.plot.ly/documentation/all_static/css/ipython-notebook-custom.css">'))

! pip install git+https://github.com/plotly/publisher.git --upgrade
import publisher
publisher.publish(
    'python-Convolution.ipynb', 'python/convolution/', 'Convolution | plotly',
    'Learn how to perform convolution between two signals in Python.',
    title='Convolution in Python | plotly',
    name='Convolution',
    language='python',
    page_type='example_index', has_thumbnail='false', display_as='signal-analysis', order=4)

Collecting git+https://github.com/plotly/publisher.git
  Cloning https://github.com/plotly/publisher.git to /private/var/folders/k_/zf24qrfn2kg710j9pdrxzrz40000gn/T/pip-07Be7Z-build
Installing collected packages: publisher
  Found existing installation: publisher 0.11
    Uninstalling publisher-0.11:
      Successfully uninstalled publisher-0.11
  Running setup.py install for publisher ... done
Successfully installed publisher-0.11
You are using pip version 9.0.3, however version 10.0.1 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.

/Users/chelsea/venv/venv2/lib/python2.7/site-packages/IPython/nbconvert.py:13: ShimWarning: The `IPython.nbconvert` package has been deprecated since IPython 4.0. You should import from nbconvert instead.
  "You should import from nbconvert instead.", ShimWarning)
/Users/chelsea/venv/venv2/lib/python2.7/site-packages/publisher/publisher.py:53: UserWarning: Did you "Save" this notebook before running this command? Remember to save, always save.
  warnings.warn('Did you "Save" this notebook before running this command? '

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