# sinc_convolution_kernel¶

static OperationNamespace.sinc_convolution_kernel(cut_off_frequency)

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).

convolve_pwc()
gaussian_convolution_kernel()