Kernels of Jackson Type and Their Application to Designing Low-Pass Filters

A sequence of linear digital low-pass filters is proposed on the basis of expansion in a Fourier series of the kernel of Jackson type $J_{3,n}(\mu)$ proportional to the cube of the Fejer kernel. In addition, exact formulas for the kernels of Jackson type $J_{l,n}(\mu)$, $l=4,5,6,$ each being proportional to the $l$-th degree of the Fejer kernel, are obtained.