`scipy.signal.windows._windows:hann`

source: /scipy/signal/windows/_windows.py :794

Signature

def hann ( M , sym = True , * , xp = None , device = None )

Summary

Return a Hann window.

Extended Summary

The Hann window is a taper formed by using a raised cosine or sine-squared with ends that touch zero.

Parameters

M : int: Number of points in the output window. If zero, an empty array is returned. An exception is thrown when it is negative.
sym : bool, optional: When True (default), generates a symmetric window, for use in filter design. When False, generates a periodic window, for use in spectral analysis.
xp : array_namespace, optional: Optional array namespace. Should be compatible with the array API standard, or supported by array-api-compat. Default: numpy
device: any: optional device specification for output. Should match one of the supported device specification in xp.

Returns

w : ndarray: The window, with the maximum value normalized to 1 (though the value 1 does not appear if M is even and sym is True).

Notes

The Hann window is defined as

w (n) = 0.5 - 0.5 cos (\frac{2 π n}{M - 1}) 0 \leq n \leq M - 1

The window was named for Julius von Hann, an Austrian meteorologist. It is also known as the Cosine Bell. It is sometimes erroneously referred to as the "Hanning" window, from the use of "hann" as a verb in the original paper and confusion with the very similar Hamming window.

Most references to the Hann 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.

Array API Standard Support

hann has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ✅                   
JAX                   ✅                     ✅                   
Dask                  ✅                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

Plot the window and its frequency response:

import numpy as np
from scipy import signal
from scipy.fft import fft, fftshift
import matplotlib.pyplot as plt

✓

window = signal.windows.hann(51)

✓

plt.plot(window)
plt.title("Hann window")
plt.ylabel("Amplitude")
plt.xlabel("Sample")

✗

plt.figure()

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A = fft(window, 2048) / (len(window)/2.0)
freq = np.linspace(-0.5, 0.5, len(A))
response = np.abs(fftshift(A / abs(A).max()))
response = 20 * np.log10(np.maximum(response, 1e-10))

✓

plt.plot(freq, response)
plt.axis([-0.5, 0.5, -120, 0])
plt.title("Frequency response of the Hann window")
plt.ylabel("Normalized magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")

✗

Aliases

scipy.signal.windows.hann