`scipy.signal.windows._windows:exponential`

source: /scipy/signal/windows/_windows.py :1757

Signature

   def     exponential (    M    ,    center    =  None   ,    tau    =  1.0   ,    sym    =  True   ,  * ,     xp    =  None   ,    device    =  None     )

Summary

Return an exponential (or Poisson) 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.
center : float, optional: Parameter defining the center location of the window function. The default value if not given is center = (M-1) / 2. This parameter must take its default value for symmetric windows.
tau : float, optional: Parameter defining the decay. For center = 0 use tau = -(M-1) / ln(x) if x is the fraction of the window remaining at the end.
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 Exponential window is defined as

w (n) = e^{- ∣ n - ce n t er ∣/ τ}

Array API Standard Support

exponential 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 symmetric window and its frequency response:

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

✓

M = 51
tau = 3.0
window = signal.windows.exponential(M, tau=tau)

✓

plt.plot(window)
plt.title("Exponential Window (tau=3.0)")
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, -35, 0])
plt.title("Frequency response of the Exponential window (tau=3.0)")
plt.ylabel("Normalized magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")

✗

This function can also generate non-symmetric windows:

tau2 = -(M-1) / np.log(0.01)
window2 = signal.windows.exponential(M, 0, tau2, False)

✓

plt.figure()
plt.plot(window2)
plt.ylabel("Amplitude")
plt.xlabel("Sample")

✗

Aliases

scipy.signal.windows.exponential