, sym=True)[source]#

Return a flat top window.

  • M (int) – Number of points in the output window. If zero or less, an empty array is returned.

  • 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 – The window, with the maximum value normalized to 1 (though the value 1 does not appear if M is even and sym is True).

Return type



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



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


Plot the window and its frequency response:

>>> from import flattop
>>> import cupy as cp
>>> from cupy.fft import fft, fftshift
>>> import matplotlib.pyplot as plt
>>> window = flattop(51)
>>> plt.plot(cupy.asnumpy(window))
>>> plt.title("Flat top window")
>>> plt.ylabel("Amplitude")
>>> plt.xlabel("Sample")
>>> plt.figure()
>>> A = fft(window, 2048) / (len(window)/2.0)
>>> freq = cupy.linspace(-0.5, 0.5, len(A))
>>> response = 20 * cupy.log10(cupy.abs(fftshift(A / cupy.abs(A).max())))
>>> plt.plot(cupy.asnumpy(freq), cupy.asnumpy(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]")