Return the Bartlett window. The Bartlett window is very similar to a triangular window, except that the end points are at zero. It is often used in signal processing for tapering a signal, without generating too much ripple in the frequency domain. Parameters --------
(M)
| 3014 | |
| 3015 | @set_module('numpy') |
| 3016 | def bartlett(M): |
| 3017 | """ |
| 3018 | Return the Bartlett window. |
| 3019 | |
| 3020 | The Bartlett window is very similar to a triangular window, except |
| 3021 | that the end points are at zero. It is often used in signal |
| 3022 | processing for tapering a signal, without generating too much |
| 3023 | ripple in the frequency domain. |
| 3024 | |
| 3025 | Parameters |
| 3026 | ---------- |
| 3027 | M : int |
| 3028 | Number of points in the output window. If zero or less, an |
| 3029 | empty array is returned. |
| 3030 | |
| 3031 | Returns |
| 3032 | ------- |
| 3033 | out : array |
| 3034 | The triangular window, with the maximum value normalized to one |
| 3035 | (the value one appears only if the number of samples is odd), with |
| 3036 | the first and last samples equal to zero. |
| 3037 | |
| 3038 | See Also |
| 3039 | -------- |
| 3040 | blackman, hamming, hanning, kaiser |
| 3041 | |
| 3042 | Notes |
| 3043 | ----- |
| 3044 | The Bartlett window is defined as |
| 3045 | |
| 3046 | .. math:: w(n) = \\frac{2}{M-1} \\left( |
| 3047 | \\frac{M-1}{2} - \\left|n - \\frac{M-1}{2}\\right| |
| 3048 | \\right) |
| 3049 | |
| 3050 | Most references to the Bartlett window come from the signal processing |
| 3051 | literature, where it is used as one of many windowing functions for |
| 3052 | smoothing values. Note that convolution with this window produces linear |
| 3053 | interpolation. It is also known as an apodization (which means "removing |
| 3054 | the foot", i.e. smoothing discontinuities at the beginning and end of the |
| 3055 | sampled signal) or tapering function. The Fourier transform of the |
| 3056 | Bartlett window is the product of two sinc functions. Note the excellent |
| 3057 | discussion in Kanasewich [2]_. |
| 3058 | |
| 3059 | References |
| 3060 | ---------- |
| 3061 | .. [1] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra", |
| 3062 | Biometrika 37, 1-16, 1950. |
| 3063 | .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", |
| 3064 | The University of Alberta Press, 1975, pp. 109-110. |
| 3065 | .. [3] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal |
| 3066 | Processing", Prentice-Hall, 1999, pp. 468-471. |
| 3067 | .. [4] Wikipedia, "Window function", |
| 3068 | https://en.wikipedia.org/wiki/Window_function |
| 3069 | .. [5] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, |
| 3070 | "Numerical Recipes", Cambridge University Press, 1986, page 429. |
| 3071 | |
| 3072 | Examples |
| 3073 | -------- |