gaussian_integral_function

static OperationNamespace.gaussian_integral_function(std, offset=0)

Creates a function that computes the integral of a normalized Gaussian.

Use this function to create a filter kernel that has a Gaussian shape. A Gaussian kernel lets pass frequencies in the range roughly determined by its width, and progressively suppresses components outside that range.

Parameters
  • std (float or Tensor) – Standard deviation \(\sigma\) of the Gaussian in the time domain. The standard deviation in the frequency domain is its inverse, so that a high value of this parameter lets fewer frequencies pass.

  • offset (float or Tensor, optional) – Center \(\mu\) of the Gaussian distribution in the time domain. Use this to offset the signal in time. Defaults to 0.

Returns

A node representing a function that computes the integral of the Gaussian function.

Return type

Function

Notes

The Gaussian that this function integrates is normalized in the time domain:

\[\frac{e^{-(t-\mu)^2/(2\sigma^2)}}{\sqrt{2\pi\sigma^2}}.\]

In the frequency domain, this Gaussian has standard deviation \(\omega_c= \sigma^{-1}\). The filter it represents therefore passes frequencies roughly in the range \([-\omega_c, \omega_c]\).