Deterministic DTFT Interpolation for Joint Frequency and Chirp-Rate Estimation: Cell-Uniform Efficiency and Threshold Analysis

Joint estimation of the frequency and chirp rate of a noisy chirp signal arises in radar, sonar, and burst satellite communications. Conventional estimators combine a coarse grid search with fine interpolation; accuracy degrades at the edges of the residual cell (the edge effect) and below the breakdown SNR (the threshold effect). This paper presents a deterministic two-stage estimator that controls both failure modes uniformly over the entire residual cell. The estimator combines a time-centered, zero-padded dechirp-FFT acquisition bank with alternating selectable-$p$ amplitude-interpolation refinements on fractional-bin DTFT samples; in the centered frame, the frequency-chirp-rate cross-term of the Fisher information vanishes. The paper derives a mean-squared-error and threshold characterization across the full SNR range, in closed form except for one calibrated scalar (an effective cell count), to our knowledge the first for the joint problem: the breakdown threshold is governed by the cell count, and its cell-position dependence is dominated by the straddle loss of the coarse FFT, which the padding bounds at 0.4 dB. An asymptotic uniformity analysis over the whole cell, including the corners, gives closed-form fixed-point variance ratios of $1.003$ and $0.998$, analytically free of the residual. A closed-form bias analysis under unmodeled jerk shows the centered chirp-rate estimate is first-order immune. Monte Carlo experiments at $N=256$ (validated at $N=32$-$512$) measure frequency- and chirp-rate-axis efficiencies with median $1.03$ and worst case $1.07$ over $144$ cell positions at $-5$ dB. Threshold predictions hold within $1.0$ dB on four held-out configurations. The dechirp-FFT bank is fully parallel, and each of the four refinement iterations evaluates three DTFT samples per axis; under fixed operating conditions, per-estimate latency is constant at $O(N\log N)$ cost.

M3GCLR: Multi-View Mini-Max Infinite Skeleton-Data Game Contrastive Learning For Skeleton-Based Action Recognition

In recent years, contrastive learning has drawn significant attention as an effective approach to reducing reliance on labeled data. However, existing methods for self-supervised skeleton-based action recognition still face three major limitations: insufficient modeling of view discrepancies, lack of effective adversarial mechanisms, and uncontrollable augmentation perturbations. To tackle these issues, we propose the Multi-view Mini-Max infinite skeleton-data Game Contrastive Learning for skeleton-based action Recognition (M3GCLR), a game-theoretic contrastive framework. First, we establish the Infinite Skeleton-data Game (ISG) model and the ISG equilibrium theorem, and further provide a rigorous proof, enabling mini-max optimization based on multi-view mutual information. Then, we generate normal-extreme data pairs through multi-view rotation augmentation and adopt temporally averaged input as a neutral anchor to achieve structural alignment, thereby explicitly characterizing perturbation strength. Next, leveraging the proposed equilibrium theorem, we construct a strongly adversarial mini-max skeleton-data game to encourage the model to mine richer action-discriminative information. Finally, we introduce the dual-loss equilibrium optimizer to optimize the game equilibrium, allowing the learning process to maximize action-relevant information while minimizing encoding redundancy, and we prove the equivalence between the proposed optimizer and the ISG model. Extensive Experiments show that M3GCLR achieves three-stream 82.1%, 85.8% accuracy on NTU RGB+D 60 (X-Sub, X-View) and 72.3%, 75.0% accuracy on NTU RGB+D 120 (X-Sub, X-Set). On PKU-MMD Part I and II, it attains 89.1%, 45.2% in three-stream respectively, all results matching or outperforming state-of-the-art performance. Ablation studies confirm the effectiveness of each component.

DoGCLR: Dominance-Game Contrastive Learning Network for Skeleton-Based Action Recognition

Existing self-supervised contrastive learning methods for skeleton-based action recognition often process all skeleton regions uniformly, and adopt a first-in-first-out (FIFO) queue to store negative samples, which leads to motion information loss and non-optimal negative sample selection. To address these challenges, this paper proposes Dominance-Game Contrastive Learning network for skeleton-based action Recognition (DoGCLR), a self-supervised framework based on game theory. DoGCLR models the construction of positive and negative samples as a dynamic Dominance Game, where both sample types interact to reach an equilibrium that balances semantic preservation and discriminative strength. Specifically, a spatio-temporal dual weight localization mechanism identifies key motion regions and guides region-wise augmentations to enhance motion diversity while maintaining semantics. In parallel, an entropy-driven dominance strategy manages the memory bank by retaining high entropy (hard) negatives and replacing low-entropy (weak) ones, ensuring consistent exposure to informative contrastive signals. Extensive experiments are conducted on NTU RGB+D and PKU-MMD datasets. On NTU RGB+D 60 X-Sub/X-View, DoGCLR achieves 81.1%/89.4% accuracy, and on NTU RGB+D 120 X-Sub/X-Set, DoGCLR achieves 71.2%/75.5% accuracy, surpassing state-of-the-art methods by 0.1%, 2.7%, 1.1%, and 2.3%, respectively. On PKU-MMD Part I/Part II, DoGCLR performs comparably to the state-of-the-art methods and achieves a 1.9% higher accuracy on Part II, highlighting its strong robustness on more challenging scenarios.