`scipy.signal.windows._windows:lanczos`

source: /scipy/signal/windows/_windows.py :2241

Signature

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

Summary

Return a Lanczos window also known as a sinc window.

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 Lanczos window is defined as

w (n) = s in c (\frac{2 n}{M - 1} - 1)

where

s in c (x) = \frac{sin ( π x )}{π x}

The Lanczos window has reduced Gibbs oscillations and is widely used for filtering climate timeseries with good properties in the physical and spectral domains.

Array API Standard Support

lanczos 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

import numpy as np
from scipy.signal.windows import lanczos
from scipy.fft import fft, fftshift
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1)
window = lanczos(51)

✓

ax.plot(window)
ax.set_title("Lanczos window")
ax.set_ylabel("Amplitude")
ax.set_xlabel("Sample")

✗

fig.tight_layout()
plt.show()

✓

and its frequency response:

fig, ax = plt.subplots(1)
A = fft(window, 2048) / (len(window)/2.0)
freq = np.linspace(-0.5, 0.5, len(A))
response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))

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ax.plot(freq, response)
ax.set_xlim(-0.5, 0.5)
ax.set_ylim(-120, 0)
ax.set_title("Frequency response of the lanczos window")
ax.set_ylabel("Normalized magnitude [dB]")
ax.set_xlabel("Normalized frequency [cycles per sample]")

✗

fig.tight_layout()
plt.show()

✓