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.

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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

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N = 100
window = create_window(N)

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plt.plot(window)
plt.title("Uniform window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")

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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

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Parzen Window

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N = 100
window = create_window(N, window_type='parzen')

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plt.plot(window)
plt.title("Parzen window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")

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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]")

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Hamming Window

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N = 50
window = create_window(N, window_type='hamming')

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plt.plot(window)
plt.title("Hamming window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")

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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]")

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Hanning Window

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N = 50
window = create_window(N, window_type='hanning')

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plt.plot(window)
plt.title("Hanning window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")

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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

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Traingular Window

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N = 50
window = create_window(N, window_type='triangular')

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plt.plot(window)
plt.title("Traingualr window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")

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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]")

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Welch Window

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N = 50
window = create_window(N, window_type='welch')

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plt.plot(window)
plt.title("Welch window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")

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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

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Blackmann’s Window

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N = 50
window = create_window(N, window_type='blackmann')

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plt.plot(window)
plt.title("Blackmann window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")

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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]")

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Flat Top Window

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N = 50
window = create_window(N, window_type='flat-top')

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plt.plot(window)
plt.title("Flat-top window")
plt.ylabel("Amplitude")
plt.xlabel("Sample Number (n)")

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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]")

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