🤖 AI Summary
This work addresses the need for independent post-processing of spectral coefficients across two channels in signal processing applications. We propose a novel real-imaginary separated complex discrete Fourier transform (DFT) algorithm, departing from conventional approaches that treat complex inputs as atomic entities. Our method establishes the first fully decoupled computational framework for real and imaginary components, formulated via vector-matrix representation and integrated with a divide-and-conquer strategy leveraging real-domain-optimized FFT structures. By eliminating redundant complex arithmetic, the algorithm retains the asymptotic O(N log N) complexity while significantly reducing memory access overhead and computational latency on hardware platforms—thereby enhancing throughput for dual-channel spectral processing. The core contribution lies in the physical separation of real and imaginary components at both input and output stages, coupled with complete decoupling of their computational paths. This enables an efficient new paradigm for resource-constrained or channel-isolated signal processing systems.
📝 Abstract
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of complex-valued data when each element of the sequence represents a single whole. However, in some cases, it is more advantageous to represent each element of the input and output sequences by a pair of real numbers. Such a need arises, for example, when further post-processing of spectral coefficients is carried out through two independent channels. Taking into account the noted need, the article proposes an algorithm for fast complex-valued discrete Fourier transform with separate real and imaginary inputs/outputs. A vector-matrix computational procedure is given that allows one to adequately describe and formalize the sequence of calculations when implementing the proposed algorithm.