numpy.bartlett

numpy.bartlett(M) [source]

Возвращает окно Бартлетта.

Окно Бартлетта очень похоже на треугольное окно, за исключением того, что конечные точки равны нулю. Оно часто используется в обработке сигналов для обрезания сигнала без генерации чрезмерных колебаний в частотной области.

Параметры

Mint

Число точек в выходном окне. Если значение равно или меньше нуля, возвращается пустой массив.

Возвращает

outarray

Треугольное окно, с максимальным значением, нормированным до единицы (значение единица появляется только если число выборок нечётное), с первыми и последними выборками, равными нулю.

См. также

blackman, hamming, hanning, kaiser

Примечания

Окно Бартлетта определяется как

<img alt="w(n) = \frac{2}{M-1} \left( \frac{M-1}{2} - \left|n - \frac{M-1}{2}\right| \right)" src="data:image/svg+xml;base64,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

Большинство ссылок на окно Бартлетта взяты из литературы по обработке сигналов, где оно используется как одна из многих функций окон для сглаживания значений. Обратите внимание, что свёртка с этим окном даёт линейную интерполяцию. Оно также известно как функция аподизации (что означает «удаление стопы», т.е. сглаживание разрывов в начале и конце выборочного сигнала) или функция обрезания. Преобразование Фурье окна Бартлетта является произведением двух функций синус-кардинале. Обратите внимание на отличное обсуждение в Kanasewich.

Ссылки

1

М.С. Бартлетт, «Периодограмма анализа и непрерывные спектры», Biometrika 37, 1-16, 1950.

2

Э.Р. Канасевич, «Анализ временных рядов в геофизике», Издательство Университета Альберты, 1975, стр. 109-110.

3

А.В. Опенгейм и Р.В. Шафер, «Цифровая обработка сигналов», Prentice-Hall, 1999, стр. 468-471.

4

Википедия, «Функция окна», https://en.wikipedia.org/wiki/Window_function

5

У.Х. Пресс, Б.П. Фланнери, С.А. Теукольский и У.Т. Веттеринг, «Численные рецепты», Издательство Кембриджского университета, 1986, стр. 429.

Примеры

>>> import matplotlib.pyplot as plt
>>> np.bartlett(12)
array([ 0.        ,  0.18181818,  0.36363636,  0.54545455,  0.72727273, # may vary
        0.90909091,  0.90909091,  0.72727273,  0.54545455,  0.36363636,
        0.18181818,  0.        ])

Постройте окно и его частотную характеристику (требуются SciPy и matplotlib):

>>> from numpy.fft import fft, fftshift
>>> window = np.bartlett(51)
>>> plt.plot(window)
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.title("Bartlett window")
Text(0.5, 1.0, 'Bartlett window')
>>> plt.ylabel("Amplitude")
Text(0, 0.5, 'Amplitude')
>>> plt.xlabel("Sample")
Text(0.5, 0, 'Sample')
>>> plt.show()

>>> plt.figure()
<Figure size 640x480 with 0 Axes>
>>> A = fft(window, 2048) / 25.5
>>> mag = np.abs(fftshift(A))
>>> freq = np.linspace(-0.5, 0.5, len(A))
>>> with np.errstate(divide='ignore', invalid='ignore'):
...     response = 20 * np.log10(mag)
...
>>> response = np.clip(response, -100, 100)
>>> plt.plot(freq, response)
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.title("Frequency response of Bartlett window")
Text(0.5, 1.0, 'Frequency response of Bartlett window')
>>> plt.ylabel("Magnitude [dB]")
Text(0, 0.5, 'Magnitude [dB]')
>>> plt.xlabel("Normalized frequency [cycles per sample]")
Text(0.5, 0, 'Normalized frequency [cycles per sample]')
>>> _ = plt.axis('tight')
>>> plt.show()

<img alt="../../_images/numpy-bartlett-1_01_00.png" src="data:image/png;base64,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