# elephant.kernels.GaussianKernel¶

class elephant.kernels.GaussianKernel(sigma, invert=False)[source]

Class for gaussian kernels.

$K(t) = (\frac{1}{\sigma \sqrt{2 \pi}}) \exp(-\frac{t^2}{2 \sigma^2})$

with $$\sigma$$ being the standard deviation.

The parameter invert has no effect on symmetric kernels.

Examples

from elephant import kernels
import quantities as pq
import numpy as np
import matplotlib.pyplot as plt

time_array = np.linspace(-3, 3, num=100) * pq.s
kernel = kernels.GaussianKernel(sigma=1*pq.s)
kernel_time = kernel(time_array)
plt.plot(time_array, kernel_time)
plt.title("GaussianKernel with sigma=1s")
plt.xlabel("time, s")
plt.ylabel("kernel, 1/s")
plt.show()

__init__(sigma, invert=False)

Methods

 __init__(sigma[, invert]) boundary_enclosing_area_fraction(fraction) Calculates the boundary $$b$$ so that the integral from $$-b$$ to $$b$$ encloses a certain fraction of the integral over the complete kernel. cdf(time) Cumulative Distribution Function, CDF. icdf(fraction) Inverse Cumulative Distribution Function, ICDF, also known as a quantile. is_symmetric() True for symmetric kernels and False otherwise (asymmetric kernels). median_index(times) Estimates the index of the Median of the kernel.

Attributes

 min_cutoff Half width of the kernel.