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)
| 2909 | |
| 2910 | @set_module('numpy') |
| 2911 | def blackman(M): |
| 2912 | """ |
| 2913 | Return the Blackman window. |
| 2914 | |
| 2915 | The Blackman window is a taper formed by using the first three |
| 2916 | terms of a summation of cosines. It was designed to have close to the |
| 2917 | minimal leakage possible. It is close to optimal, only slightly worse |
| 2918 | than a Kaiser window. |
| 2919 | |
| 2920 | Parameters |
| 2921 | ---------- |
| 2922 | M : int |
| 2923 | Number of points in the output window. If zero or less, an empty |
| 2924 | array is returned. |
| 2925 | |
| 2926 | Returns |
| 2927 | ------- |
| 2928 | out : ndarray |
| 2929 | The window, with the maximum value normalized to one (the value one |
| 2930 | appears only if the number of samples is odd). |
| 2931 | |
| 2932 | See Also |
| 2933 | -------- |
| 2934 | bartlett, hamming, hanning, kaiser |
| 2935 | |
| 2936 | Notes |
| 2937 | ----- |
| 2938 | The Blackman window is defined as |
| 2939 | |
| 2940 | .. math:: w(n) = 0.42 - 0.5 \\cos(2\\pi n/M) + 0.08 \\cos(4\\pi n/M) |
| 2941 | |
| 2942 | Most references to the Blackman window come from the signal processing |
| 2943 | literature, where it is used as one of many windowing functions for |
| 2944 | smoothing values. It is also known as an apodization (which means |
| 2945 | "removing the foot", i.e. smoothing discontinuities at the beginning |
| 2946 | and end of the sampled signal) or tapering function. It is known as a |
| 2947 | "near optimal" tapering function, almost as good (by some measures) |
| 2948 | as the kaiser window. |
| 2949 | |
| 2950 | References |
| 2951 | ---------- |
| 2952 | Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, |
| 2953 | Dover Publications, New York. |
| 2954 | |
| 2955 | Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. |
| 2956 | Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471. |
| 2957 | |
| 2958 | Examples |
| 2959 | -------- |
| 2960 | >>> import matplotlib.pyplot as plt |
| 2961 | >>> np.blackman(12) |
| 2962 | array([-1.38777878e-17, 3.26064346e-02, 1.59903635e-01, # may vary |
| 2963 | 4.14397981e-01, 7.36045180e-01, 9.67046769e-01, |
| 2964 | 9.67046769e-01, 7.36045180e-01, 4.14397981e-01, |
| 2965 | 1.59903635e-01, 3.26064346e-02, -1.38777878e-17]) |
| 2966 | |
| 2967 | Plot the window and the frequency response: |
| 2968 |