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scipy.signal.windows.

# flattop

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

  Return a flat top window.

  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

  Flat top windows are used for taking accurate measurements of signal amplitude in the frequency domain, with minimal scalloping error from the center of a frequency bin to its edges, compared to others. This is a 5th-order cosine window, with the 5 terms optimized to make the main lobe maximally flat. [1]

  Array API Standard Support

  `flattop` 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]

  D’Antona, Gabriele, and A. Ferrero, “Digital Signal Processing for Measurement Systems”, Springer Media, 2006, p. 70 DOI:10.1007/0-387-28666-7.

  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.flattop(51)
      >>> plt.plot(window)
      >>> plt.title("Flat top 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 flat top window")
      >>> plt.ylabel("Normalized magnitude [dB]")
      >>> plt.xlabel("Normalized frequency [cycles per sample]")