Window functions

Stingray now has a bunch of window functions that can be used for various applications in signal processing.

Windows available include: 1. Uniform or Rectangular Window 2. Parzen window 3. Hamming window 4. Hanning Window 5. Triangular window 6. Welch Window 7. Blackmann Window 8. Flat-top Window

All windows are available in stingray.utils package and called be used by calling create_window function. Below are some of the examples demonstrating different window functions.

In [64]:
from stingray.utils import create_window

from scipy.fftpack import fft, fftshift, fftfreq
import numpy as np

import matplotlib.pyplot as plt
%matplotlib inline

create_window function in stingray.utils takes two parameters.

  1. N : Number of data points in the window
  2. window_type : Type of window to create. Default is uniform.

Uniform Window

In [65]:
N = 100
window = create_window(N)
In [66]:
plt.plot(window)
plt.title("Uniform window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")
Out[66]:
<matplotlib.text.Text at 0x21d8f0ccc50>
../../_images/notebooks_Window_Functions_window_functions_7_1.png
In [67]:
nfft = 2048
A = fft(uniform_window,nfft ) / (len(uniform_window)/2.0)
freq = fftfreq(nfft)
response = 20 * np.log10(np.abs(fftshift(A/(abs(A).max()))))
plt.plot(freq, response)
plt.title("Frequency response of the Uniform window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
C:\Users\Haroon Rashid\Anaconda3\lib\site-packages\ipykernel\__main__.py:4: RuntimeWarning: divide by zero encountered in log10
Out[67]:
<matplotlib.text.Text at 0x21d8f1b6e10>
../../_images/notebooks_Window_Functions_window_functions_8_2.png

Parzen Window

In [68]:
N = 100
window = create_window(N, window_type='parzen')
In [69]:
plt.plot(window)
plt.title("Parzen window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")
Out[69]:
<matplotlib.text.Text at 0x21d8f1a8160>
../../_images/notebooks_Window_Functions_window_functions_11_1.png
In [70]:
nfft = 2048
A = fft(window,nfft ) / (len(window)/2.0)
freq = fftfreq(nfft)
response = 20 * np.log10(np.abs(fftshift(A/(abs(A).max()))))
plt.plot(freq, response)
plt.title("Frequency response of the Parzen window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
Out[70]:
<matplotlib.text.Text at 0x21d8f24b978>
../../_images/notebooks_Window_Functions_window_functions_12_1.png

Hamming Window

In [71]:
N = 50
window = create_window(N, window_type='hamming')
In [72]:
plt.plot(window)
plt.title("Hamming window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")
Out[72]:
<matplotlib.text.Text at 0x21d8f360ba8>
../../_images/notebooks_Window_Functions_window_functions_15_1.png
In [73]:
nfft = 2048
A = fft(window,nfft ) / (len(window)/2.0)
freq = fftfreq(nfft)
response = 20 * np.log10(np.abs(fftshift(A/(abs(A).max()))))
plt.plot(freq, response)
plt.title("Frequency response of the Hamming window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
Out[73]:
<matplotlib.text.Text at 0x21d8f2f6fd0>
../../_images/notebooks_Window_Functions_window_functions_16_1.png

Hanning Window

In [74]:
N = 50
window = create_window(N, window_type='hanning')
In [75]:
plt.plot(window)
plt.title("Hanning window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")
Out[75]:
<matplotlib.text.Text at 0x21d8f34f470>
../../_images/notebooks_Window_Functions_window_functions_19_1.png
In [76]:
nfft = 2048
A = fft(window,nfft ) / (len(window)/2.0)
freq = fftfreq(nfft)
response = 20 * np.log10(np.abs(fftshift(A/(abs(A).max()))))
plt.plot(freq, response)
plt.title("Frequency response of the Hanning window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
C:\Users\Haroon Rashid\Anaconda3\lib\site-packages\ipykernel\__main__.py:4: RuntimeWarning: divide by zero encountered in log10
Out[76]:
<matplotlib.text.Text at 0x21d8f4715f8>
../../_images/notebooks_Window_Functions_window_functions_20_2.png

Traingular Window

In [77]:
N = 50
window = create_window(N, window_type='triangular')
In [78]:
plt.plot(window)
plt.title("Traingualr window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")
Out[78]:
<matplotlib.text.Text at 0x21d8f4397b8>
../../_images/notebooks_Window_Functions_window_functions_23_1.png
In [79]:
nfft = 2048
A = fft(window,nfft ) / (len(window)/2.0)
freq = fftfreq(nfft)
response = 20 * np.log10(np.abs(fftshift(A/(abs(A).max()))))
plt.plot(freq, response)
plt.title("Frequency response of the Triangular window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
Out[79]:
<matplotlib.text.Text at 0x21d8f534470>
../../_images/notebooks_Window_Functions_window_functions_24_1.png

Welch Window

In [80]:
N = 50
window = create_window(N, window_type='welch')
In [81]:
plt.plot(window)
plt.title("Welch window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")
Out[81]:
<matplotlib.text.Text at 0x21d8f629eb8>
../../_images/notebooks_Window_Functions_window_functions_27_1.png
In [82]:
nfft = 2048
A = fft(window,nfft ) / (len(window)/2.0)
freq = fftfreq(nfft)
response = 20 * np.log10(np.abs(fftshift(A/(abs(A).max()))))
plt.plot(freq, response)
plt.title("Frequency response of the Welch window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
C:\Users\Haroon Rashid\Anaconda3\lib\site-packages\ipykernel\__main__.py:4: RuntimeWarning: divide by zero encountered in log10
Out[82]:
<matplotlib.text.Text at 0x21d8f738080>
../../_images/notebooks_Window_Functions_window_functions_28_2.png

Blackmann’s Window

In [83]:
N = 50
window = create_window(N, window_type='blackmann')
In [84]:
plt.plot(window)
plt.title("Blackmann window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")
Out[84]:
<matplotlib.text.Text at 0x21d8f6b92e8>
../../_images/notebooks_Window_Functions_window_functions_31_1.png
In [85]:
nfft = 2048
A = fft(window,nfft ) / (len(window)/2.0)
freq = fftfreq(nfft)
response = 20 * np.log10(np.abs(fftshift(A/(abs(A).max()))))
plt.plot(freq, response)
plt.title("Frequency response of the Blackmann window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
Out[85]:
<matplotlib.text.Text at 0x21d9083b2e8>
../../_images/notebooks_Window_Functions_window_functions_32_1.png

Flat Top Window

In [86]:
N = 50
window = create_window(N, window_type='flat-top')
In [87]:
plt.plot(window)
plt.title("Flat-top window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")
Out[87]:
<matplotlib.text.Text at 0x21d9081e470>
../../_images/notebooks_Window_Functions_window_functions_35_1.png
In [88]:
nfft = 2048
A = fft(window,nfft ) / (len(window)/2.0)
freq = fftfreq(nfft)
response = 20 * np.log10(np.abs(fftshift(A/(abs(A).max()))))
plt.plot(freq, response)
plt.title("Frequency response of the Flat-top window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
Out[88]:
<matplotlib.text.Text at 0x21d909314a8>
../../_images/notebooks_Window_Functions_window_functions_36_1.png