Show Sidebar Hide Sidebar # FFT Filters in Python

Learn how filter out the frequencies of a signal by using low-pass, high-pass and band-pass FFT filtering.

#### New to Plotly?Â¶

Plotly's Python library is free and open source! Get started by downloading the client and reading the primer.
You can set up Plotly to work in online or offline mode, or in jupyter notebooks.
We also have a quick-reference cheatsheet (new!) to help you get started!

#### ImportsÂ¶

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

In :
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 DataÂ¶

An 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:

In :
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')

Out:

#### Plot the DataÂ¶

Let's look at our data in its raw form before doing any filtering.

In :
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')

Out:

#### Low-Pass FilterÂ¶

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.

In :
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')

Out:

#### High-Pass FilterÂ¶

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.

In :
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')

Out:

#### Band-Pass FilterÂ¶

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.

In :
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')

Out: 