Convolution

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Imports

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

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.

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')

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.

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')

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)
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