{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The Hanning window is defined as" } ] }, { "__type": "Math", "__tag": 4058, "value": "w(n) = 0.5 - 0.5\\cos\\left(\\frac{2\\pi{n}}{M-1}\\right)\\qquad 0 \\leq n \\leq M-1" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The Hanning was named for Julius von Hann, an Austrian meteorologist. It is also known as the Cosine Bell. Some authors prefer that it be called a Hann window, to help avoid confusion with the very similar Hamming window." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Most references to the Hanning window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. 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[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. 106-108.", ".. [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." ], "qa": "numpy:hanning", "arbitrary": [], "local_refs": [ "M", "out" ] }