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Plotly's Python library is free and open source! Get started by downloading the client and reading the primer.
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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 signalAn FFT Filter is a process that involves mapping a time signal from time-space to frequency-space in which frequency becomes an axis. By mapping to this space, we can get a better picture for how much of which frequency is in the original time signal and we can ultimately cut some of these frequencies out to remap back into time-space. Such filter types include low-pass, where lower frequencies are allowed to pass and higher ones get cut off -, high-pass, where higher frequencies pass, and band-pass, which selects only a narrow range or "band" of frequencies to pass through.
Let us import some stock data to apply FFT Filtering:
data = pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/wind_speed_laurel_nebraska.csv')
df = data[0:10]
table = ff.create_table(df)
py.iplot(table, filename='wind-data-sample')Let's look at our data in its raw form before doing any filtering.
trace1 = go.Scatter(
x=list(range(len(list(data['10 Min Std Dev'])))),
y=list(data['10 Min Std Dev']),
mode='lines',
name='Wind Data'
)
layout = go.Layout(
showlegend=True
)
trace_data = [trace1]
fig = go.Figure(data=trace_data, layout=layout)
py.iplot(fig, filename='wind-raw-data-plot')A Low-Pass Filter is used to remove the higher frequencies in a signal of data.
fc is the cutoff frequency as a fraction of the sampling rate, and b is the transition band also as a function of the sampling rate. N must be an odd number in our calculation as well.
fc = 0.1
b = 0.08
N = int(np.ceil((4 / b)))
if not N % 2: N += 1
n = np.arange(N)
sinc_func = np.sinc(2 * fc * (n - (N - 1) / 2.))
window = 0.42 - 0.5 * np.cos(2 * np.pi * n / (N - 1)) + 0.08 * np.cos(4 * np.pi * n / (N - 1))
sinc_func = sinc_func * window
sinc_func = sinc_func / np.sum(sinc_func)
s = list(data['10 Min Std Dev'])
new_signal = np.convolve(s, sinc_func)
trace1 = go.Scatter(
x=list(range(len(new_signal))),
y=new_signal,
mode='lines',
name='Low-Pass Filter',
marker=dict(
color='#C54C82'
)
)
layout = go.Layout(
title='Low-Pass Filter',
showlegend=True
)
trace_data = [trace1]
fig = go.Figure(data=trace_data, layout=layout)
py.iplot(fig, filename='fft-low-pass-filter')Similarly a High-Pass Filter will remove the lower frequencies from a signal of data.
Again, fc is the cutoff frequency as a fraction of the sampling rate, and b is the transition band also as a function of the sampling rate. N must be an odd number.
Only by performing a spectral inversion afterwards after setting up our Low-Pass Filter will we get the High-Pass Filter.
fc = 0.1
b = 0.08
N = int(np.ceil((4 / b)))
if not N % 2: N += 1
n = np.arange(N)
sinc_func = np.sinc(2 * fc * (n - (N - 1) / 2.))
window = np.blackman(N)
sinc_func = sinc_func * window
sinc_func = sinc_func / np.sum(sinc_func)
# reverse function
sinc_func = -sinc_func
sinc_func[int((N - 1) / 2)] += 1
s = list(data['10 Min Std Dev'])
new_signal = np.convolve(s, sinc_func)
trace1 = go.Scatter(
x=list(range(len(new_signal))),
y=new_signal,
mode='lines',
name='High-Pass Filter',
marker=dict(
color='#424242'
)
)
layout = go.Layout(
title='High-Pass Filter',
showlegend=True
)
trace_data = [trace1]
fig = go.Figure(data=trace_data, layout=layout)
py.iplot(fig, filename='fft-high-pass-filter')The Band-Pass Filter will allow you to reduce the frequencies outside of a defined range of frequencies. We can think of it as low-passing and high-passing at the same time.
In the example below, fL and fH are the low and high cutoff frequencies respectively as a fraction of the sampling rate.
fL = 0.1
fH = 0.3
b = 0.08
N = int(np.ceil((4 / b)))
if not N % 2: N += 1 # Make sure that N is odd.
n = np.arange(N)
# low-pass filter
hlpf = np.sinc(2 * fH * (n - (N - 1) / 2.))
hlpf *= np.blackman(N)
hlpf = hlpf / np.sum(hlpf)
# high-pass filter
hhpf = np.sinc(2 * fL * (n - (N - 1) / 2.))
hhpf *= np.blackman(N)
hhpf = hhpf / np.sum(hhpf)
hhpf = -hhpf
hhpf[int((N - 1) / 2)] += 1
h = np.convolve(hlpf, hhpf)
s = list(data['10 Min Std Dev'])
new_signal = np.convolve(s, h)
trace1 = go.Scatter(
x=list(range(len(new_signal))),
y=new_signal,
mode='lines',
name='Band-Pass Filter',
marker=dict(
color='#BB47BE'
)
)
layout = go.Layout(
title='Band-Pass Filter',
showlegend=True
)
trace_data = [trace1]
fig = go.Figure(data=trace_data, layout=layout)
py.iplot(fig, filename='fft-band-pass-filter')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-FFT-Filters.ipynb', 'python/fft-filters/', 'FFT Filters | plotly',
'Learn how filter out the frequencies of a signal by using low-pass, high-pass and band-pass FFT filtering.',
title='FFT Filters in Python | plotly',
name='FFT Filters',
language='python',
page_type='example_index', has_thumbnail='false', display_as='signal-analysis', order=2)