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hamming(M)

The Hamming window is a taper formed by using a weighted cosine.

Notes

The Hamming window is defined as

$$w(n) = 0.54 - 0.46cos\left(\frac{2\pi{n}}{M-1}\right)\qquad 0 \leq n \leq M-1$$

The Hamming was named for R. W. Hamming, an associate of J. W. Tukey and is described in Blackman and Tukey. It was recommended for smoothing the truncated autocovariance function in the time domain. Most references to the Hamming window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function.

Parameters

M : int: Number of points in the output window. If zero or less, an empty array is returned.

Returns

out : ndarray: The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd).

Return the Hamming window.

Examples

>>> np.hamming(12)
array([ 0.08      ,  0.15302337,  0.34890909,  0.60546483,  0.84123594, # may vary
        0.98136677,  0.98136677,  0.84123594,  0.60546483,  0.34890909,
        0.15302337,  0.08      ])

Plot the window and the frequency response:

>>> import matplotlib.pyplot as plt
... from numpy.fft import fft, fftshift
... window = np.hamming(51)
... plt.plot(window)
[<matplotlib.lines.Line2D object at 0x...>]

>>> plt.title("Hamming window")
Text(0.5, 1.0, 'Hamming 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))
... 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 Hamming window")
Text(0.5, 1.0, 'Frequency response of Hamming 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()

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

matplotlib.axes._axes.Axes.cohere matplotlib.pyplot.psd numpy.kaiser matplotlib.pyplot.angle_spectrum matplotlib.axes._axes.Axes.magnitude_spectrum numpy.bartlett matplotlib.pyplot.cohere numpy.hanning matplotlib.mlab.cohere matplotlib.mlab.specgram numpy.blackman matplotlib.pyplot.magnitude_spectrum matplotlib.axes._axes.Axes.psd matplotlib.pyplot.phase_spectrum matplotlib.pyplot.csd matplotlib.axes._axes.Axes.csd matplotlib.mlab.csd matplotlib.axes._axes.Axes.angle_spectrum matplotlib.axes._axes.Axes.phase_spectrum matplotlib.pyplot.specgram matplotlib.axes._axes.Axes.specgram matplotlib.mlab.psd

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