`scipy.signal.windows._windows:general_hamming`

source: /scipy/signal/windows/_windows.py :1027

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, $α$
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

w (n) = α - (1 - α) cos (\frac{2 π n}{M - 1}) 0 \leq n \leq M - 1

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

Array API Standard Support

general_hamming has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ✅                   
JAX                   ✅                     ✅                   
Dask                  ✅                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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

✓

fig1, spatial_plot = plt.subplots()

✓

spatial_plot.set_title("Generalized Hamming Windows")
spatial_plot.set_ylabel("Amplitude")
spatial_plot.set_xlabel("Sample")

✗

fig2, freq_plot = plt.subplots()

✓

freq_plot.set_title("Frequency Responses")
freq_plot.set_ylabel("Normalized magnitude [dB]")
freq_plot.set_xlabel("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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Aliases

scipy.signal.windows.general_hamming

Referenced by

This package

release:1.1.0-notes