flopscope.

flopscope.numpy.hanning

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

Return the Hanning window.

Adapted from NumPy docs np.hanning

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

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

The Hanning 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, shape(M,)

The window, with the maximum value normalized to one (the value one appears only if M is odd).

See also

Notes

The Hanning window is defined as

w(n)=0.5−0.5cos⁡(2πnM−1)0≤n≤M−1w(n) = 0.5 - 0.5\cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1

The Hanning was named for Julius von Hann, an Austrian meteorologist. It is also known as the Cosine Bell. Some authors prefer that it be called a Hann window, to help avoid confusion with the very similar Hamming window.

Most references to the Hanning 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. 106-108.
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.hanning(12)
array([0.        , 0.07937323, 0.29229249, 0.57115742, 0.82743037,
       0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249,
       0.07937323, 0.        ])

Plot the window and its frequency response.

Plot Source.
import matplotlib.pyplot as plt
from flops.fft import fft, fftshift
window = flops.hanning(51)
plt.plot(window)
plt.title("Hann 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))
with flops.errstate(divide='ignore', invalid='ignore'):
    response = 20 * flops.log10(mag)
response = flops.clip(response, -100, 100)
plt.plot(freq, response)
plt.title("Frequency response of the Hann window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
plt.axis('tight')
plt.show()