gaussian_convolution_kernel

Graph.gaussian_convolution_kernel(std, offset=0)

Creates a convolution kernel representing a normalized Gaussian.

Use this kernel to allow frequencies in the range roughly determined by its width, and progressively suppress 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 Gaussian function to use in a convolution.

Return type

ConvolutionKernel

Notes

The Gaussian that this node represents 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 \([-\omega_c, \omega_c]\).

See also

convolve_pwc()

Create an Stf by convolving a Pwc with a kernel.

sinc_convolution_kernel()

Create a convolution kernel representing the sinc function.