Return the Hanning window. The Hanning window is a taper formed by using a weighted cosine. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : ndarray, shape(M,)
(M)
| 3254 | |
| 3255 | @set_module('numpy') |
| 3256 | def hanning(M): |
| 3257 | """ |
| 3258 | Return the Hanning window. |
| 3259 | |
| 3260 | The Hanning window is a taper formed by using a weighted cosine. |
| 3261 | |
| 3262 | Parameters |
| 3263 | ---------- |
| 3264 | M : int |
| 3265 | Number of points in the output window. If zero or less, an |
| 3266 | empty array is returned. |
| 3267 | |
| 3268 | Returns |
| 3269 | ------- |
| 3270 | out : ndarray, shape(M,) |
| 3271 | The window, with the maximum value normalized to one (the value |
| 3272 | one appears only if `M` is odd). |
| 3273 | |
| 3274 | See Also |
| 3275 | -------- |
| 3276 | bartlett, blackman, hamming, kaiser |
| 3277 | |
| 3278 | Notes |
| 3279 | ----- |
| 3280 | The Hanning window is defined as |
| 3281 | |
| 3282 | .. math:: w(n) = 0.5 - 0.5\\cos\\left(\\frac{2\\pi{n}}{M-1}\\right) |
| 3283 | \\qquad 0 \\leq n \\leq M-1 |
| 3284 | |
| 3285 | The Hanning was named for Julius von Hann, an Austrian meteorologist. |
| 3286 | It is also known as the Cosine Bell. Some authors prefer that it be |
| 3287 | called a Hann window, to help avoid confusion with the very similar |
| 3288 | Hamming window. |
| 3289 | |
| 3290 | Most references to the Hanning window come from the signal processing |
| 3291 | literature, where it is used as one of many windowing functions for |
| 3292 | smoothing values. It is also known as an apodization (which means |
| 3293 | "removing the foot", i.e. smoothing discontinuities at the beginning |
| 3294 | and end of the sampled signal) or tapering function. |
| 3295 | |
| 3296 | References |
| 3297 | ---------- |
| 3298 | .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power |
| 3299 | spectra, Dover Publications, New York. |
| 3300 | .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", |
| 3301 | The University of Alberta Press, 1975, pp. 106-108. |
| 3302 | .. [3] Wikipedia, "Window function", |
| 3303 | https://en.wikipedia.org/wiki/Window_function |
| 3304 | .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, |
| 3305 | "Numerical Recipes", Cambridge University Press, 1986, page 425. |
| 3306 | |
| 3307 | Examples |
| 3308 | -------- |
| 3309 | >>> import numpy as np |
| 3310 | >>> np.hanning(12) |
| 3311 | array([0. , 0.07937323, 0.29229249, 0.57115742, 0.82743037, |
| 3312 | 0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249, |
| 3313 | 0.07937323, 0. ]) |
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