Window functions

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

Windows available include:

Uniform or Rectangular Window
Parzen window
Hamming window
Hanning Window
Triangular window
Welch Window
Blackmann Window
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.

N : Number of data points in the window
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>



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>

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>



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>

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>



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>

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>



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>

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>



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>

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>



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>

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>



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>

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>



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>