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scipy.signal.windows.

# hamming

scipy.signal.windows.hamming(M, sym=True, *, xp=None, device=None)

  Return a Hamming window.

  The Hamming window is a taper formed by using a raised cosine with non-zero endpoints, optimized to minimize the nearest side lobe.

  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.

    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 Hamming window is defined as

  \[w(n) = 0.54 - 0.46 \cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1\]

  The Hamming was named for R. W. Hamming, an associate of J. W. Tukey and is described in Blackman and Tukey. It was recommended for smoothing the truncated autocovariance function in the time domain. Most references to the Hamming window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means “removing the foot”, i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function.

  Array API Standard Support

  `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 Support for the array API standard for more information.

  References

  [1]

  Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York.

  [2]

  E.R. Kanasewich, “Time Sequence Analysis in Geophysics”, The University of Alberta Press, 1975, pp. 109-110.

  [3]

  Wikipedia, “Window function”, https://en.wikipedia.org/wiki/Window_function

  [4]

  W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, “Numerical Recipes”, Cambridge University Press, 1986, page 425.

  Examples

  Plot the window and its frequency response:

      >>> import numpy as np
      >>> from scipy import signal
      >>> from scipy.fft import fft, fftshift
      >>> import matplotlib.pyplot as plt

      >>> window = signal.windows.hamming(51)
      >>> plt.plot(window)
      >>> plt.title("Hamming window")
      >>> plt.ylabel("Amplitude")
      >>> plt.xlabel("Sample")

      >>> plt.figure()
      >>> 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())))
      >>> plt.plot(freq, response)
      >>> plt.axis([-0.5, 0.5, -120, 0])
      >>> plt.title("Frequency response of the Hamming window")
      >>> plt.ylabel("Normalized magnitude [dB]")
      >>> plt.xlabel("Normalized frequency [cycles per sample]")