`scipy.signal.windows._windows:chebwin`

source: /scipy/signal/windows/_windows.py :1559

Signature

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

Summary

Return a Dolph-Chebyshev 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.
at : float: Attenuation (in dB).
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 always normalized to 1

Notes

This window optimizes for the narrowest main lobe width for a given order M and sidelobe equiripple attenuation at, using Chebyshev polynomials. It was originally developed by Dolph to optimize the directionality of radio antenna arrays.

Unlike most windows, the Dolph-Chebyshev is defined in terms of its frequency response:

W (k) = \frac{cos { M cos ^{- 1} [ β cos ( \frac{π k}{M} )]}}{cosh [ M cosh ^{- 1} ( β )]}

where

β = cosh [\frac{1}{M} cosh^{- 1} (1 0^{\frac{A}{20}})]

and 0 <= abs(k) <= M-1. A is the attenuation in decibels (at).

The time domain window is then generated using the IFFT, so power-of-two M are the fastest to generate, and prime number M are the slowest.

The equiripple condition in the frequency domain creates impulses in the time domain, which appear at the ends of the window.

Array API Standard Support

chebwin 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.chebwin(51, at=100)

✓

plt.plot(window)
plt.title("Dolph-Chebyshev window (100 dB)")
plt.ylabel("Amplitude")
plt.xlabel("Sample")

✗

plt.figure()

✗

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())))

✓

plt.plot(freq, response)
plt.axis([-0.5, 0.5, -120, 0])
plt.title("Frequency response of the Dolph-Chebyshev window (100 dB)")
plt.ylabel("Normalized magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")

✗

Aliases

scipy.signal.windows.chebwin