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bundles / scipy 2.0.0.dev0+git20260907.41eeb59 / scipy / signal / windows / _windows / general_hamming

function

scipy.signal.windows._windows:general_hamming

source: build-install/usr/lib/python3.14/site-packages/scipy/signal/windows/_windows.py:1190

Signature

def general_hamming(M, alpha, sym = True, *, xp = None, device = None)

Summary

Return a generalized Hamming window.

Extended Summary

The generalized Hamming window is constructed by multiplying a rectangular window by one period of a cosine function [1].

Parameters

M : int

Number of points in the output window. If zero, an empty array is returned. An exception is thrown when it is negative.

alpha : float

The window coefficient,

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.

xp : array_namespace, optional

Optional array namespace. Should be compatible with the array API standard, or supported by array-api-compat. Default: numpy

device : any

optional device specification for output. Should match one of the supported device specification in xp.

Returns

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

Both the common Hamming window and Hann window are special cases of the generalized Hamming window with = 0.54 and = 0.5, respectively [2].

Examples

The Sentinel-1A/B Instrument Processing Facility uses generalized Hamming windows in the processing of spaceborne Synthetic Aperture Radar (SAR) data [3]_. The facility uses various values for the :math:`\alpha` parameter based on operating mode of the SAR instrument. Some common :math:`\alpha` values include 0.75, 0.7 and 0.52 [4]_. As an example, we plot these different windows. 
import numpy as np
from scipy.signal.windows import general_hamming
from scipy.fft import fft, fftshift
import matplotlib.pyplot as plt
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fig1, spatial_plot = plt.subplots()
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spatial_plot.set_title("Generalized Hamming Windows")
spatial_plot.set_ylabel("Amplitude")
spatial_plot.set_xlabel("Sample")
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Text(0.5, 0, 'Sample')

fig2, freq_plot = plt.subplots()
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freq_plot.set_title("Frequency Responses")
freq_plot.set_ylabel("Normalized magnitude [dB]")
freq_plot.set_xlabel("Normalized frequency [cycles per sample]")
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Text(0.5, 0, 'Normalized frequency [cycles per sample]')

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")
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<matplotlib.legend.Legend object at 0x7f3f43c63a10>

See also

hamming
hann

Aliases

  • scipy.signal.windows.general_hamming

Referenced by

This package