digital signal processing

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.

To address the challenge of detecting 6-kHz narrowband transient components in real-time signals, this paper proposes an FPGA-optimized wavelet spectral analysis method. Unlike conventional FFT-based approaches, which suffer from inherent trade-offs between time-frequency resolution and latency, our method fully hardware-implements the Daubechies wavelet transform—including fixed-point arithmetic design, pipelined convolution, and on-chip RAM caching—on a Xilinx Artix-7 FPGA. The architecture achieves both high precision and ultra-low latency: under a 250 MS/s input throughput, detection latency is below 5 μs, with total system power consumption under 1.2 W. This work overcomes the real-time detection bottleneck for narrowband transients on resource-constrained embedded platforms and establishes a reusable hardware acceleration paradigm for edge intelligence in high-frequency dynamic signal sensing.

This study addresses the limitations of conventional image enhancement, filtering, and pattern recognition—namely, heavy reliance on manual feature engineering and insufficient real-time performance—by proposing a theory-driven, end-to-end machine learning framework. Methodologically, it is the first to systematically integrate discrete Fourier transform (DFT), Z-transform, and continuous Fourier analysis into deep learning pipelines, synergistically coupling them with convolutional neural networks (CNNs) and classical digital filtering algorithms to enable frequency-domain-guided automated feature extraction and real-time joint signal–image processing. The key contributions include: (i) development of an extensible Python framework; (ii) average PSNR improvement of 3.2 dB in image enhancement and noise suppression tasks; and (iii) 40% acceleration in feature extraction efficiency. This work establishes a novel paradigm for AI-powered real-time computer vision that simultaneously ensures high performance and interpretability.

This work addresses the lack of effective online experimental platforms in signal processing education and engineering talent development. To bridge this gap, the authors developed and have continuously refined J-DSP, a web-based simulation environment that pioneered the migration of the original Java-based DSP toolkit to an HTML5 architecture, enabling cross-platform— including mobile—accessibility. The platform integrates advanced topics such as digital filter design, FFT-based spectral analysis, machine learning for signal classification, and quantum Fourier transform. Having operated reliably for 25 years, J-DSP has been widely adopted in university courses and National Science Foundation–funded programs, including REU, IRES, and RET initiatives, significantly advancing the modernization of signal processing pedagogy and fostering STEM workforce development.

Traditional discrete Fourier transform (DFT) is constrained by uniform sampling and fixed-length sequences, rendering it inadequate for non-uniformly sampled, missing-data, or ultra-long signals. To address this, we propose the Extended Discrete Fourier Transform (EDFT), which formulates spectral estimation as an optimization problem minimizing the Fourier integral residual. EDFT adaptively constructs frequency-domain basis functions without requiring equispaced time-domain sampling or identical sequence lengths. Our method integrates iterative optimization, explicit Fourier integral constraints, and adaptive inverse DFT-based signal reconstruction. It enables high-resolution spectral estimation, time-domain extrapolation, missing-data imputation, and direct processing of non-uniformly sampled signals. Compared to DFT, EDFT substantially broadens the applicability of Fourier analysis while preserving theoretical rigor and computational feasibility.

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 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.

This study investigates the circuit complexity bounds of fundamental Boolean operators in digital circuit design. By systematically analyzing known upper and lower complexity bounds for canonical Boolean functions—such as counters, adders, encoders, and multiplexers—and integrating both classical and modern Boolean function synthesis techniques, the work proposes efficient circuit synthesis strategies. Emphasizing the interplay between theoretical complexity and practical synthesis efficiency for basic operators, this research not only consolidates existing results but also provides a theoretical foundation and practical guidance for optimizing the design of complex digital circuits.

This study addresses a fundamental challenge in system identification: distinguishing spurious eigenvalues arising from limited data from those genuinely reflecting the underlying system dynamics. To this end, the paper introduces—for the first time—the probabilistic sampling pseudospectrum \( P(\lambda) \) and its computationally efficient estimator \( \hat{P}(\lambda) \). By leveraging resampling and statistical inference, this framework quantifies the uncertainty of eigenvalues across the complex plane. The proposed approach provides a general and rigorous statistical criterion for data-driven methods such as Dynamic Mode Decomposition and subspace identification, substantially enhancing the reliability of identifying true dynamical modes from noisy, finite-length observations.

Traditional global correlation analysis struggles to characterize multiscale dynamic interdependencies between signals. To address this, we propose a wavelet-based multiscale cross-correlation analysis framework. Methodologically, we integrate orthogonal and undecimated discrete wavelet transforms to construct Pearson- and Kendall-type wavelet cross-correlation graphs, partial wavelet correlations, and additive wavelet correlation measures—balancing time-frequency localization with statistical robustness. Theoretically, we generalize the definition and properties of wavelet correlation coefficients. Empirically, simulation studies demonstrate superior sensitivity to time-varying and nonstationary correlation structures; real-data applications successfully uncover cross-frequency coupling patterns. Results show that our approach accurately captures localized, heterogeneous correlation features between two signals across distinct frequency scales, significantly enhancing interpretability and applicability in multiscale dependency modeling.