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Convolution in Python

Learn how to perform convolution between two signals in Python.

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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
from plotly.tools import FigureFactory 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 [5]:
x = range(15)
y_saw = signal.sawtooth(t=x)

data_sample = list(stock_data['SBUX'][0:100])
data_sample2 = list(stock_data['AAPL'][0:100])
convolve_y = signal.convolve(y_saw, data_sample2)

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

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

trace3 = go.Scatter(
    x = range(len(convolve_y)),
    y = convolve_y,
    mode = 'lines',
    name = 'Convolution'
)

data = [trace1, trace2, trace3]
py.iplot(data, filename='convolution-of-two-signals')
Out[5]:
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