Creates a convolution kernel representing the sinc function.
Use this kernel to eliminate frequencies 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 the sinc function to use in a convolution.
- Return type
ConvolutionKernel
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).