flopscope.

flopscope.numpy.hamming

fnp.hamming(M)[flopscope source][numpy source]

Return the Hamming window.

Adapted from NumPy docs np.hamming

Areacore
Typecustom
NumPy Refnp.hamming
Cost
16×nn
Flopscope Context

Hamming window. Cost: n (one cosine per sample).

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).

See also

Notes

The Hamming window is defined as

w(n)=0.54−0.46cos⁡(2πnM−1)0≤n≤M−1w(n) = 0.54 - 0.46\cos\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.

References

footnote
1

Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
spectra, Dover Publications, New York.
footnote
2

E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
University of Alberta Press, 1975, pp. 109-110.
footnote
3

Wikipedia, "Window function",
https://en.wikipedia.org/wiki/Window_function
footnote
4

W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
"Numerical Recipes", Cambridge University Press, 1986, page 425.

Examples

>>> import flopscope.numpy as fnp
>>> flops.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.

Plot Source.
import matplotlib.pyplot as plt
from flops.fft import fft, fftshift
window = flops.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 = flops.abs(fftshift(A))
freq = flops.linspace(-0.5, 0.5, len(A))
response = 20 * flops.log10(mag)
response = flops.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()