convolution.md

jupyter

jupytext kernelspec plotly notebook_metadata_filter text_representation all extension format_name format_version jupytext_version .md markdown 1.1 1.1.1 display_name language name Python 2 python python2 description display_as has_thumbnail language layout name order page_type permalink thumbnail Learn how to perform convolution between two signals in Python. signal-analysis false python base Convolution 4 example_index python/convolution/ /images/static-image

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Imports

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

importplotly.plotlyaspyimportplotly.graph_objsasgoimportplotly.figure_factoryasffimportnumpyasnpimportpandasaspdimportscipyfromscipyimportsignal

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')

fromIPython.displayimportdisplay, HTMLdisplay(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">')) ! pipinstallgit+https://github.com/plotly/publisher.git--upgradeimportpublisherpublisher.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)