Real-Time Discrete Fractional Fourier Transform Using Metamaterial Coupled Lines Network

Abstract

Discrete fractional Fourier transforms (DFrFTs) are universal mathematical tools in signal processing, communications, and microwave sensing. Despite the excessive applications of DFrFT, the implementation of corresponding fractional orders in the baseband signal often leads to bulky, power-hungry, and high-latency systems. In this article, we present a passive metamaterial coupled lines network (MCLN) that performs the analog DFrFT in real-time at microwave frequencies. The proposed MCLN consists of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$</tex-math> </inline-formula> parallel microstrip transmission lines (TLs) in which adjacent TLs are loaded with interdigital capacitors to enhance the coupling level. We show that with the proper design of the coupling coefficients between adjacent channels, the MCLN can perform an M-point DFrFT of an arbitrary fractional order that can be designed through the length of the network. In the context of real-time signal processing for the realization of DFrFT, we design, model, simulate, and implement a 16 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> 16 MCLN and experimentally demonstrate the performance of the proposed structure. The proposed innovative approach is versatile and is capable to be used in various applications where DFrFT is an essential tool. The proposed design scheme based on MCLN is scalable across the frequency spectrum and can be applied to the millimeter and submillimeter wave systems.