Return the Blackman window. The Blackman window is a taper formed by using the first three terms of a summation of cosines. It was designed to have close to the minimal leakage possible. It is close to optimal, only slightly worse than a Kaiser window. Parameters ----
(M)
| 3048 | |
| 3049 | @set_module('numpy') |
| 3050 | def blackman(M): |
| 3051 | """ |
| 3052 | Return the Blackman window. |
| 3053 | |
| 3054 | The Blackman window is a taper formed by using the first three |
| 3055 | terms of a summation of cosines. It was designed to have close to the |
| 3056 | minimal leakage possible. It is close to optimal, only slightly worse |
| 3057 | than a Kaiser window. |
| 3058 | |
| 3059 | Parameters |
| 3060 | ---------- |
| 3061 | M : int |
| 3062 | Number of points in the output window. If zero or less, an empty |
| 3063 | array is returned. |
| 3064 | |
| 3065 | Returns |
| 3066 | ------- |
| 3067 | out : ndarray |
| 3068 | The window, with the maximum value normalized to one (the value one |
| 3069 | appears only if the number of samples is odd). |
| 3070 | |
| 3071 | See Also |
| 3072 | -------- |
| 3073 | bartlett, hamming, hanning, kaiser |
| 3074 | |
| 3075 | Notes |
| 3076 | ----- |
| 3077 | The Blackman window is defined as |
| 3078 | |
| 3079 | .. math:: w(n) = 0.42 - 0.5 \\cos(2\\pi n/M) + 0.08 \\cos(4\\pi n/M) |
| 3080 | |
| 3081 | Most references to the Blackman window come from the signal processing |
| 3082 | literature, where it is used as one of many windowing functions for |
| 3083 | smoothing values. It is also known as an apodization (which means |
| 3084 | "removing the foot", i.e. smoothing discontinuities at the beginning |
| 3085 | and end of the sampled signal) or tapering function. It is known as a |
| 3086 | "near optimal" tapering function, almost as good (by some measures) |
| 3087 | as the Kaiser window. |
| 3088 | |
| 3089 | References |
| 3090 | ---------- |
| 3091 | .. [1] Blackman, R.B. and Tukey, J.W., (1958) |
| 3092 | The measurement of power spectra, Dover Publications, New York. |
| 3093 | .. [2] Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. |
| 3094 | Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471. |
| 3095 | |
| 3096 | Examples |
| 3097 | -------- |
| 3098 | >>> import numpy as np |
| 3099 | >>> import matplotlib.pyplot as plt |
| 3100 | >>> np.blackman(12) |
| 3101 | array([-1.38777878e-17, 3.26064346e-02, 1.59903635e-01, # may vary |
| 3102 | 4.14397981e-01, 7.36045180e-01, 9.67046769e-01, |
| 3103 | 9.67046769e-01, 7.36045180e-01, 4.14397981e-01, |
| 3104 | 1.59903635e-01, 3.26064346e-02, -1.38777878e-17]) |
| 3105 | |
| 3106 | Plot the window and the frequency response. |
| 3107 |
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