Multi-stage cascaded structure for large-point FFT based on memristor crossbar arrays

Considering the significant challenges posed by array size limitations and finite memristor conductive states, this paper presents a multi-stage cascaded fast Fourier transform (FFT) architecture based on memristors, designed to enable scalable, efficient large-point (more than 1k points) discrete Fourier transform operations. This architecture employs the Cooley–Tukey algorithm to decompose large-point FFTs into multiple stages of smaller-point FFTs. Integrating the Winograd algorithm minimizes multiplicative complexity, thereby reducing demands on memristor conductance states. In addition, a twiddle-factor encoding method is proposed to achieve precise representation with fewer conductive states. The proposed multi-stage cascaded circuit architecture exhibits high flexibility, supporting arbitrary 2N-point FFT operations and providing a robust framework for large-scale signal processing applications.