Polynomial Trigonometric Kernels and Their Application to Designing Low-Pass Filters

This study continues the effort made in [1] to develop out digital low-pass filters with an improved amplitude-frequency characteristic. As in [1], the main attention is given to using the expansion in a Fourier series of polynomial Jackson-type kernels for designing the filters. Pulse responses of a new four-filter set are proposed. These newly designed filters significantly surpass those suggested in [1], concerning the level of the side lobes of the amplitude-frequency characteristic side lobes. In addition, we also indicate the possibility of an alternative approach to designing low-pass filters with the use of expansion in a Fourier series of the polynomial kernels of Jackson–Vallée Poussin type.