fft implementation

Spectrum prediction in dynamic spectrum access (DSA) faces significant challenges due to strong noise interference and severe time-frequency domain feature entanglement. To address these issues, this paper proposes the Spectrum Forecasting via Fractional Fourier Domain (SFFP) framework—the first to incorporate adaptive fractional Fourier transform (AFrFT) into spectrum modeling. By learning optimal transform orders, SFFP achieves maximal signal-noise separation in the fractional domain. Furthermore, it integrates complex-valued neural networks with adaptive filtering to enable end-to-end feature enhancement and trend prediction directly within the fractional domain. Experimental evaluation on real-world spectrum datasets demonstrates that SFFP consistently outperforms state-of-the-art time-frequency domain methods, achieving 12.6%–23.4% improvements in prediction accuracy while exhibiting superior robustness under noisy and nonstationary conditions. This work establishes a novel paradigm for intelligent spectrum management in highly dynamic wireless environments.

To address the dual challenges of stringent computational constraints and hard real-time requirements in embedded real-time spectrum analysis, this work presents the first complete fixed-point 36-point FFT implementation on the Nuvoton NUC140V2 microcontroller (ARM Cortex-M0, 72 MHz), based on the Prime Factor Algorithm (PFA). Unlike conventional Cooley–Tukey FFTs, PFA exploits prime-factor decomposition and divide-and-conquer DFT restructuring to eliminate both twiddle-factor look-up tables and complex multiplications, thereby drastically reducing arithmetic overhead. Leveraging C-language fixed-point arithmetic and assembly-level optimization of critical execution paths, the implementation achieves a runtime of 127 μs and consumes only 288 bytes of memory. This work establishes a new paradigm for high-throughput, low-overhead spectral analysis on resource-constrained MCUs, satisfying deterministic latency requirements in diverse real-time audio processing applications.

Designing signal processing algorithms for ultra-low-power hardware demands maximizing energy efficiency under stringent constraints on parallelism and on-chip memory. To address this, we propose four key techniques: (1) accuracy-guaranteed quasi-spline piecewise polynomial approximation, balancing numerical precision with integer-arithmetic compatibility; (2) conflict-free streaming FFT scheduling and self-sorting FFT variants tailored for multi-bank single-port memory; (3) memory-aware parallelization of Schur decomposition and Toeplitz system solving; and (4) a CMOS power-model-driven, mixed-radix FFT co-optimization framework. Theoretically, we establish constructive theorems and derive tight bounds on parallel and memory complexity. Practically, we deliver implementable scheduling strategies and energy-efficiency–area trade-off curves. These contributions jointly enable high-energy-efficiency domain-specific accelerator design for resource-constrained embedded systems.

This work addresses the high computational complexity of key operations—parallel FIR filtering, polynomial modular multiplication, and pointwise multiplication in DFT/NTT domains—across signal processing and cryptography. We propose the first cross-domain algorithmic equivalence framework grounded in fast convolution structures. By systematically generalizing Cook–Toom and Winograd convolution algorithms to short-length iterative settings, we unify the modeling of these four operations and reveal their underlying algebraic isomorphism. The framework enables direct structural transfer and reuse across domains, substantially reducing multiplicative complexity: it achieves 1.5–3× speedup in critical subroutines of post-quantum cryptographic schemes (e.g., Kyber, Dilithium) and homomorphic encryption schemes (e.g., BFV, CKKS). This bridges theoretical and engineering gaps between digital signal processing and modern cryptographic algorithm design, establishing a generic optimization paradigm for efficient cryptographic implementations.

To address the challenge of jointly modeling time-structure coupling dynamics in time-varying graph signals—i.e., vertex-located continuous-time series—within non-Euclidean domains, this paper proposes the Joint Vertex-Time Fractional Fourier Transform (JVF-TFT). For the first time, the fractional Fourier transform is extended to the joint vertex-time domain via the tensor product of the graph Fourier transform and the classical fractional Fourier transform, yielding a tunable-order parametric joint spectral representation. This framework enables sparse representation and localized analysis of non-stationary, non-Euclidean signals while achieving joint spectral energy concentration. Experiments on traffic flow and electroencephalography (EEG) data demonstrate that JVF-TFT significantly outperforms conventional decoupled-domain methods in signal reconstruction accuracy, noise robustness, compression ratio, and discriminative performance.

This work proposes a novel mixture-of-experts (MoE) adapter that overcomes the limitations of existing parameter-efficient fine-tuning methods, which are confined to fixed spatial or frequency domains and struggle to adapt to task-, layer-, or token-specific optimal representations. By introducing the fractional Fourier transform (FrFT) into the MoE architecture for the first time, each expert is equipped with a learnable FrFT order, enabling continuous interpolation between spatial and frequency domains and dynamic selection of the most compact low-rank update space. This design naturally induces expert decorrelation through learnable domain selection, substantially enhancing multi-task compositionality with minimal computational overhead. Experiments on LLaMA-3.1-8B and Qwen2.5-7B demonstrate consistent superiority over strong baselines such as FlyLoRA and FourierMoE across commonsense, mathematical, coding, and knowledge-intensive tasks, while maintaining low active parameter counts and revealing interpretable patterns of order specialization at both task and layer levels.

This work addresses the limitations of conventional fixed-point FFT implementations in optical OFDM transceivers, which suffer from insufficient dynamic range and numerical robustness, while standard floating-point arithmetic incurs excessive hardware overhead. The authors propose a cross-layer co-design methodology that introduces, for the first time, a customized low-precision floating-point format (11/12 bits) into the FFT core of optical OFDM systems, jointly optimizing numerical representation, arithmetic units, and overall system performance. Post-layout implementation in 12nm FinFET technology, coupled with BER and Eb/N0 simulations, demonstrates that under a 128 Gbit/s, 256-point FFT configuration, the proposed design reduces power consumption by up to 19.8% and area by up to 12.0% compared to typical fixed-point implementations, while achieving BER performance close to that of a 32-bit floating-point baseline—effectively balancing energy efficiency, numerical accuracy, and hardware cost.

This work addresses the challenge of efficiently implementing high-precision fast Fourier transforms (FFTs) on modern processors that favor low-precision, high-throughput arithmetic. It introduces, for the first time, the Ozaki high-precision computation framework into the FFT domain, leveraging Bluestein’s algorithm to reformulate the FFT as a cyclic convolution. The method computes split components exactly using number-theoretic transforms (NTT) in low-precision arithmetic and reconstructs the high-precision result via the Chinese Remainder Theorem. A novel NTT-domain accumulation strategy is proposed to drastically reduce the number of required NTT calls. Experimental results demonstrate that double-precision FFTs can be achieved with only 64–96 invocations of 32-bit NTTs, yielding relative errors lower than those of both FFTW and Triple-Single approaches while maintaining consistent accuracy across varying transform lengths.

This work addresses the performance degradation of Chinese Remainder Theorem (CRT)-based sparse FFT algorithms when moduli are not pairwise coprime, a scenario in which worst-case complexity can exceed that of the classical FFT. Focusing on $k$-sparse signals, the paper establishes the first adversarial lower bound of $\Omega(k^2)$ under this setting. To mitigate this issue, the authors propose a robust sparse FFT framework that employs lightweight certificates—such as bucket occupancy and candidate set size—to verify reconstruction reliability. If verification succeeds, the algorithm achieves a complexity of $O(\sqrt{N} \log N + kN)$; otherwise, it safely falls back to dense FFT with guaranteed $O(N \log N)$ complexity, ensuring worst-case performance never degrades below that of the classical FFT.

This work addresses the longstanding trade-off between performance and latency in large finite impulse response (FIR) filters commonly used in image, video, and audio processing. The authors propose a unified design language that abstracts multirate filtering, recursive filtering, and filter decomposition into composable primitives. By combining program-space search with gradient-based optimization of continuous parameters, the framework automatically synthesizes Pareto-optimal approximate filtering algorithms. This approach enables, for the first time, the systematic integration of diverse fast filtering techniques and fully automated code generation, producing vectorized and parallelized C++ implementations. Evaluated across multiple mainstream image and audio tasks, the generated filters consistently outperform existing methods in both speed and accuracy.