We present a theoretical background of how symmetric polynomials with roots on the unit circle can be useful for improving aliasing rejection in comb decimation filters. First, the theorem on symmetric polynomials with zeros on the unit circle is introduced. The theorem states the condition that the zeros of the symmetric polynomial remain on the unit circle if the polynomial middle coefficient is changed. Next, we present how to change the middle coefficient to design a simple multiplierless filter called a zero-separation (ZS) filter. The ZS filter separates the double polynomial zeros. The characteristics and the procedure for designing ZS filters are presented and illustrated with examples. 

In continuation, we present the comb decimation filter and how the ZS filter separates double comb zeros. The separation of doubled comb zeros improves comb aliasing rejection. All steps are illustrated with examples.

Gordana Jovanovic Dolecek received a BSc and Ph.D. from the University of Sarajevo, Bosnia and Herzegovina, and an MSc degree from the University of Beograd, Serbia. She was a professor with the Faculty of Electrical Engineering, University of Sarajevo, from 1969 to 1993. From 1993 to 1995, she worked as a researcher at the Institute Mihajlo Pupin, Belgrade, Serbia. In 1995, she joined the Institute INAOE, Department for Electronics, Puebla, Mexico, where she works as a full professor. She was a visiting researcher with UCSB, Santa Barbara, USA, in 2001-2002, 2006, with SDSU San Diego, USA, in 2008-2009, and with UCLA, Los Angeles, USA, in 2015-2016.

She is the author/coauthor of over 80 journals and 400 conference papers. She is the author of the textbook G. Jovanovic Dolecek, “Random Signals and Processes Primer with MATLAB,” Springer NY: 2013, and editor of book G. Jovanovic Dolecek (Ed), ”Advances in Multirate Systems,” Springer, NY, 2017, and pioneer book G. Jovanovic Dolecek (Ed), “Multirate Systems: Design and Applications,” IGP, Hershey, USA, 2001.

She is a member of the Mexican Academy of Sciences, SNI of Mexico, and Life Senior Member, IEEE.

She was the Associate Editor for IEEE Transactions on Circuits and Systems-I: Regular Papers (2016-2023), IEEE Circuits and Systems Magazine (2022-2023), and IEEE Transactions on Circuits and Systems II: Express Brief (2016-2023).

She is the Senior Associate Editor for IEEE Transactions on Circuits and Systems-II: Express Brief, Associate Editor for IET Signal Processing, and a member of the Editorial Board for the journal Facta Universitatis, Series: Electronics and Energetics.

She was a Guest Editor for the Special Issue “Advances of Wireless Communications Using Machine Learning and Deep Learning Techniques”, for MDPI Applied Science in 2023, Guest Editor with N. Cho for the Special Issue “Advances in Image Processing Using Machine Learning Techniques,” for IET Signal Processing, in 2022, one of the Guest Editors for Special Issue:” Digital Divide: Closing the Gap,” IEEE Communication Magazine, 2021, and one of the Guest Editors for Special Issue: “Advanced Techniques on Multirate Signal Processing for Digital Information Processing”, for IET Signal Processing, 2013.

Recognitions:

• In 2024, she received a prestigious IEEE CASS John Choma educational award.

• In 2024, she received recognition as a Best Associate Editor of IEEE TCAS II journal for 2023.

• In 2023, she received recognition as a Best Associate Editor of IEEE TCAS I journal for 2022.

• In 2022, she was the recipient of the IEEE Mexico Puebla award for her achievement in electrical engineering, “Mujer en Ciencia” (“Women in Science”).

• In 2022, she received recognition as a Best Associate Editor of IEEE TCAS I journal for 2020-2021.

• In 2012, she received the Science and Technology Puebla State Award for her achievement in electronics.