# scipy.signal.windows.general_hamming¶

scipy.signal.windows.general_hamming(M, alpha, sym=True)[source]

Return a generalized Hamming window.

The generalized Hamming window is constructed by multiplying a rectangular window by one period of a cosine function .

Parameters: M : int Number of points in the output window. If zero or less, an empty array is returned. alpha : float The window coefficient, $$\alpha$$ sym : bool, optional When True (default), generates a symmetric window, for use in filter design. When False, generates a periodic window, for use in spectral analysis. w : ndarray The window, with the maximum value normalized to 1 (though the value 1 does not appear if M is even and sym is True).

Notes

The generalized Hamming window is defined as

$w(n) = \alpha - \left(1 - \alpha\right) \cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1$

Both the common Hamming window and Hann window are special cases of the generalized Hamming window with $$\alpha$$ = 0.54 and $$\alpha$$ = 0.5, respectively .

References

  (1, 2) DSPRelated, “Generalized Hamming Window Family”, https://www.dsprelated.com/freebooks/sasp/Generalized_Hamming_Window_Family.html
  (1, 2) Wikipedia, “Window function”, http://en.wikipedia.org/wiki/Window_function
  (1, 2) Riccardo Piantanida ESA, “Sentinel-1 Level 1 Detailed Algorithm Definition”, https://sentinel.esa.int/documents/247904/1877131/Sentinel-1-Level-1-Detailed-Algorithm-Definition
  (1, 2) Matthieu Bourbigot ESA, “Sentinel-1 Product Definition”, https://sentinel.esa.int/documents/247904/1877131/Sentinel-1-Product-Definition

Examples

The Sentinel-1A/B Instrument Processing Facility uses generalized Hamming windows in the processing of spaceborne Synthetic Aperture Radar (SAR) data . The facility uses various values for the $$\alpha$$ parameter based on operating mode of the SAR instrument. Some common $$\alpha$$ values include 0.75, 0.7 and 0.52 . As an example, we plot these different windows.

>>> from scipy.signal.windows import general_hamming
>>> from scipy.fftpack import fft, fftshift
>>> import matplotlib.pyplot as plt

>>> plt.figure()
>>> plt.title("Generalized Hamming Windows")
>>> plt.ylabel("Amplitude")
>>> plt.xlabel("Sample")
>>> spatial_plot = plt.axes()

>>> plt.figure()
>>> plt.title("Frequency Responses")
>>> plt.ylabel("Normalized magnitude [dB]")
>>> plt.xlabel("Normalized frequency [cycles per sample]")
>>> freq_plot = plt.axes()

>>> for alpha in [0.75, 0.7, 0.52]:
...     window = general_hamming(41, alpha)
...     spatial_plot.plot(window, label="{:.2f}".format(alpha))
...     A = fft(window, 2048) / (len(window)/2.0)
...     freq = np.linspace(-0.5, 0.5, len(A))
...     response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
...     freq_plot.plot(freq, response, label="{:.2f}".format(alpha))
>>> freq_plot.legend(loc="upper right")
>>> spatial_plot.legend(loc="upper right")  #### Previous topic

scipy.signal.windows.general_gaussian

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scipy.signal.windows.hamming