Simple Trick: Leveraging Certain Symmetrical Polynomials with All Zeros on the Unit Circle to Enhance Alias Rejection in Comb Decimation Filters [tips & Tricks]

This paper presents a simple trick to increase aliasing rejection in comb decimation filters, based on modified symmetrical polynomials with unit coefficients, where the middle coefficients are set to zero. Two theorems prove that the zeros of the modified polynomials are all on the unit circle, for odd and even decimation factors. The modified polynomials are used to create modified combs, thus introducing various zeros either in the vicinity or inside the comb folding bands. As a result, the folding bands become wider and with an increased alias attenuation. An additional modified comb is introduced to improve alias attenuation further. The method is illustrated with two examples -one for odd and one for even decimation factors- providing a clear understanding of its application. Finally, the corresponding structure is presented, demonstrating the design's simplicity.