eriodic window, for use in spectral analysis. 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]_ 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]") )