sinc_integral_function

static OperationNamespace.sinc_integral_function(cut_off_frequency)

Creates a function that computes the integral of the sinc function.

Use this function to create a filter kernel that eliminates frequencies that are above a certain cut-off.

Parameters

cut_off_frequency (float or Tensor) – Upper limit \(\omega_c\) of the range of frequencies that you want to preserve. The filter eliminates components of the signal that have higher frequencies.

Returns

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

Return type

Function

Notes

The range of frequencies that this kernel lets pass is \([-\omega_c, \omega_c]\). After a Fourier transform to convert from frequency domain to time domain, this becomes:

\[\frac{1}{2\pi} \int_{-\omega_c}^{\omega_c} \mathrm{d}\omega e^{i \omega t} = \frac{\sin(\omega_c t)}{\pi t}.\]

The function on the right side of the equation is the sinc function. Its integral is the sine integral function (Si).