Return the Hamming window. The Hamming 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 The
(M)
| 3236 | |
| 3237 | @set_module('numpy') |
| 3238 | def hamming(M): |
| 3239 | """ |
| 3240 | Return the Hamming window. |
| 3241 | |
| 3242 | The Hamming window is a taper formed by using a weighted cosine. |
| 3243 | |
| 3244 | Parameters |
| 3245 | ---------- |
| 3246 | M : int |
| 3247 | Number of points in the output window. If zero or less, an |
| 3248 | empty array is returned. |
| 3249 | |
| 3250 | Returns |
| 3251 | ------- |
| 3252 | out : ndarray |
| 3253 | The window, with the maximum value normalized to one (the value |
| 3254 | one appears only if the number of samples is odd). |
| 3255 | |
| 3256 | See Also |
| 3257 | -------- |
| 3258 | bartlett, blackman, hanning, kaiser |
| 3259 | |
| 3260 | Notes |
| 3261 | ----- |
| 3262 | The Hamming window is defined as |
| 3263 | |
| 3264 | .. math:: w(n) = 0.54 - 0.46\\cos\\left(\\frac{2\\pi{n}}{M-1}\\right) |
| 3265 | \\qquad 0 \\leq n \\leq M-1 |
| 3266 | |
| 3267 | The Hamming was named for R. W. Hamming, an associate of J. W. Tukey |
| 3268 | and is described in Blackman and Tukey. It was recommended for |
| 3269 | smoothing the truncated autocovariance function in the time domain. |
| 3270 | Most references to the Hamming window come from the signal processing |
| 3271 | literature, where it is used as one of many windowing functions for |
| 3272 | smoothing values. It is also known as an apodization (which means |
| 3273 | "removing the foot", i.e. smoothing discontinuities at the beginning |
| 3274 | and end of the sampled signal) or tapering function. |
| 3275 | |
| 3276 | References |
| 3277 | ---------- |
| 3278 | .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power |
| 3279 | spectra, Dover Publications, New York. |
| 3280 | .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The |
| 3281 | University of Alberta Press, 1975, pp. 109-110. |
| 3282 | .. [3] Wikipedia, "Window function", |
| 3283 | https://en.wikipedia.org/wiki/Window_function |
| 3284 | .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, |
| 3285 | "Numerical Recipes", Cambridge University Press, 1986, page 425. |
| 3286 | |
| 3287 | Examples |
| 3288 | -------- |
| 3289 | >>> np.hamming(12) |
| 3290 | array([ 0.08 , 0.15302337, 0.34890909, 0.60546483, 0.84123594, # may vary |
| 3291 | 0.98136677, 0.98136677, 0.84123594, 0.60546483, 0.34890909, |
| 3292 | 0.15302337, 0.08 ]) |
| 3293 | |
| 3294 | Plot the window and the frequency response: |
| 3295 |