`numpy:hamming`

source: /numpy/lib/_function_base_impl.py :3345

Signature

def hamming ( M )

Summary

Return the Hamming window.

Extended Summary

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

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).

Notes

The Hamming window is defined as

w (n) = 0.54 - 0.46 cos (\frac{2 π n}{M - 1}) 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.

Examples

import numpy as np

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np.hamming(12)

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Plot the window and the frequency response. .. plot:: :include-source: import matplotlib.pyplot as plt from numpy.fft import fft, fftshift window = np.hamming(51) plt.plot(window) plt.title("Hamming window") plt.ylabel("Amplitude") plt.xlabel("Sample") plt.show() plt.figure() 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) plt.title("Frequency response of Hamming window") plt.ylabel("Magnitude [dB]") plt.xlabel("Normalized frequency [cycles per sample]") plt.axis('tight') plt.show()

Aliases

numpy.hamming