Time-Frequency

Most single-channel separators estimate a source by applying a real gain to the mixture in each time-frequency bin. The optimum of that format, which the oracle masks used as bounds do not attain, is the orthogonal projection of the source onto the line spanned by the mixture, its residual set by the angle between them. Locating an estimator reduces to the block structure of a real-linear operator on stacked spectra, giving a chain of four nested classes whose three larger terms match three assumptions on the prior: zero means, circularity and absence of inter-frequency coupling. Held fixed the chain is a cascade of four orthogonal projections; refitted per frame it collapses onto its first term, attributing the whole residual to one missing real parameter per bin, the phase. When the phase posterior is symmetric about the mixture direction, the minimum mean-square estimate falls back onto the line, with gain the posterior mean of the oracle gain and excess error its variance. On MUSDB18 a posterior mean under a non-circular Gaussian-mixture prior leaves the class yet stays 11.44 dB under the per-frame ceiling, which four times as many components and 7.5x the data do not close; a closed-form gate attributes some 70% of it, in decibels, to the predicted variance. The widest fixed class stays 6.70 dB under the same ceiling. Leaving the class and minimising squared error are conflicting requests: the barrier lies in the criterion rather than in the prior.

Non-professional music recordings shared online often suffer from background noise and reverberation, degrading perceived quality and limiting reuse. This paper proposes DSME, a music enhancement model based on dual time-frequency spectral representations. Within a generative adversarial framework, DSME uses short-time Fourier transform (STFT) spectra for generation and constant-Q transform (CQT) spectra for discrimination. Leveraging STFT's fixed window, invertibility, and predictability, the generator estimates clean amplitude-phase spectra from degraded inputs and reconstructs waveforms via inverse STFT. Exploiting CQT's log-frequency, variable-window structure aligned with musical octaves, we design an octave-segmented CQT discriminator. We also introduce a chroma-spectrum loss to emphasize pitch and harmonic consistency. Experiments show DSME outperforms baselines in objective and subjective tests, validating the effectiveness of the dual-spectrum approach.

Multivariate Time Series Classification (MTSC) demands models that can effectively capture complex temporal patterns across multiple scales while remaining computationally efficient. However, existing approaches generally struggle to reconcile fine-grained representation learning, especially under class imbalance and real-world constraints. In this paper, we present FreSH, a Frequency-Segmented Hierarchical Multi-Expert Framework designed to address these challenges. FreSH introduces a new perspective for MTSC by enabling adaptive, multi-scale analysis of temporal signals, allowing different aspects of the data to be modeled in a complementary and coordinated manner. By combining localized specialization with holistic context modeling, FreSH achieves strong representational capacity without incurring excessive computational overhead. An adaptive fusion strategy further enhances flexibility, enabling the model to dynamically emphasize the most informative components of the input. In addition, we incorporate a more robust optimization objective that improves learning stability across varying sample difficulties and class distributions. Extensive evaluations on 30 UEA benchmark datasets and real-world vibration data demonstrate that FreSH consistently outperforms state-of-the-art methods in classification accuracy, while substantially reducing model size and efficiency.

Learning disentangled representations is a key requirement for developing versatile, general-purpose, and sustainable models in multi-modal wearable computing. However, existing approaches do not operate as full-stack wearable processors, i.e., they do not simultaneously address task-specific classification performance, disentangled and interpretable representation learning, fusion, and generative modeling of highly heterogeneous multi-modal time series. To address this gap, we introduce Omni-modal Variational Decomposition Autoencoders (OmniDecVAEs), a framework that efficiently learns multi-purpose representations in a unified and scalable manner from arbitrarily many modalities. OmniDecVAEs extend DecVAEs by learning modality-conditioned time-frequency latent subspaces through a multi-view self-supervised decomposition loss and a shared asymmetric autoencoder (AE) architecture. Results on a challenging omni-modal human activity recognition (HAR) setting with up to thirty modalities, demonstrate the ability of OmniDecVAEs to learn full-stack wearable representations. When compared to transformer-based and VAE-based methods, OmniDecVAEs full-stack disentangled representation properties lead to accuracy improvements of 1.01% and 6.75% in activity and identity recognition, respectively. Furthermore, OmniDecVAEs synthesize realistic omni-modal time-frequency data that manifest with enhanced reconstructions (mean absolute error improves by 76.84%) and distributional similarity between real and synthetic data (maximum mean discrepancy improves by 13.85%). Our results highlight OmniDecVAEs potential as a lightweight model suitable for intelligent edge wearables and clinical healthcare, unifying processing requirements and abilities in a single model, through its enhanced representational capacity, modality-invariant spatial complexity (4.1M parameters), and real-time latency.

The increasing use of first-person-view drones in modern conflicts has created a demand for compact and reliable detection systems capable of operating in complex electromagnetic environments. These drones continuously transmit video signals through onboard video transmitters, generating radio-frequency emissions that can be exploited for early detection. This study investigates the use of lightweight convolutional neural networks for automated detection of drone signals captured by a software-defined radio-based electronic warfare framework. Samples are converted into rasterized time-domain images, providing a computationally efficient input representation suitable for embedded systems. Several custom model architectures were designed and benchmarked in terms of accuracy, model size, and inference performance using a dataset containing approximately 40,000 labeled images. In addition to offline testing, the models were integrated into a GNU Radio signal processing chain for real-time evaluation. The results show that compact models can achieve high detection accuracy while maintaining low computational requirements, making them suitable for embedded radio-frequency monitoring applications. Compared with existing spectrogram-based RF detection methods, the proposed approach eliminates frequency-domain preprocessing and achieves comparable accuracy with significantly reduced computational cost.

Generative models have changed how machine learning represents complex data distributions, especially in language and vision, yet many real-world systems are observed instead as continuous, high-dimensional, and noisy sensor time series. Existing generative modeling of sensor data, however, remains fragmented across modalities, datasets, and task formulations, limiting a systematic understanding of when, how, and why generative models succeed or fail in real-world settings. To address this gap, we introduce SensorGen, a large-scale study of sensor-signal generation spanning 14 settings across 4 domains, 7 datasets, and 12 signal modalities. Leveraging SensorGen, we systematically evaluate generative models from five major families and uncover three key findings: (1) flow-matching models provide strong overall performance across most settings; (2) signal properties matter, with demographic covariates improving longitudinal generation and time-frequency modeling improving high-frequency signal generation; and (3) generated signals have practical utility beyond visual realism, with scaling improving generation quality and synthetic data improving downstream performance. Together, SensorGen establishes a broader understanding of design choices, evaluation protocols, and failure modes in real-world sensor data generation.

Electroencephalography (EEG) foundation models aim to learn generalizable representations from large-scale brain recordings. However, the role of temporal feature extractors and whether pretrained time-series foundation models (TSFMs) can be effectively transferred to this setting remains underexplored. We conduct a controlled comparison of three temporal feature extraction strategies, including a linear baseline, a convolutional encoder, and a frozen pretrained TSFM (MOMENT), within a unified EEG foundation model. We evaluate their impact on representation quality using two downstream tasks: motor imagery and emotion recognition. Results reveal different trends across the evaluated benchmarks. On the motor imagery dataset, simple temporal representations perform competitively, whereas the emotion dataset benefits from richer temporal modeling. Although not specifically adapted to EEG, the pretrained TSFM serves as an effective temporal feature extractor, suggesting that general-purpose time-series representations can be transferred as frozen temporal feature extractors within EEG foundation models.

Recent advances in speech separation (SS) have led to compact front-end models with small parameter sizes, yet their high computational cost remains a major barrier for deployment on edge devices. To address this, we propose TF-MoE, a sparse Mixture-of-Experts (MoE) framework that enhances model capacity with almost no increase in inference cost. Our method introduces dynamic expert specialization in time and frequency dimensions through alternating time-wise and frequency-wise MoE modules, each dynamically selecting experts per frame or mel band. Built upon a mel-band-splitting Conformer backbone, TF-MoE achieves strong performance on SS tasks under low-compute settings. Experimental results demonstrate that TF-MoE consistently improves separation performance under computation cost constraints, outperforming BSRNN by +3.8 dB SDR on Libri2Mix with comparable 4.1 GMACs/s inference cost. This positions TF-MoE as a promising candidate for edge-device deployment.

Inspired by advances in natural language processing and computer vision, "time-series foundation models" (TSFMs) have recently been introduced with the promise of strong generalization across diverse time-series tasks, including forecasting, classification, and anomaly detection, as well as across domains such as healthcare, climate science, and manufacturing. However, their utility for gas-sensing data remains largely unexplored. To address this gap, this paper systematically evaluates recent TSFMs on electronic nose (E-Nose) data. In particular, we investigate whether embeddings produced by representative TSFMs, including Chronos-2 and MOMENT, provide effective representations for gas identification and concentration prediction. Specifically, we show that fine-tuning is necessary to achieve satisfactory performance on E-Nose data, and fusing TSFM embeddings with representations learned by specialized predictive models can further improve the performance, suggesting both the potential and limitations of current TSFMs for gas-sensing applications.

Self-supervised learning (SSL) has emerged as an essential paradigm for music information retrieval (MIR). While current SSL models achieve state-of-the-art performance across various MIR tasks, they typically treat audio as 1D sequences, either operating on time-domain waveforms or on flattened time-frequency-domain spectrograms. This discards the rich spatial and structural information in time-frequency representations and overlooks a fundamental intuition in music production. In particular, music is naturally represented as time-frequency grids in MIDI-based workflows, a structure that tightly corresponds to 2D spectrograms and inherently makes many MIR tasks trivial. Motivated by this intuition, we propose PupuM2D, a musical Masked Modeling Duo (M2D) model that is trained directly on 2D music spectrograms. Instead of applying masked language modeling (MLM) to 1D sequences, PupuM2D learns robust representations by predicting the latent embeddings of masked 2D music spectrogram patches from unmasked contexts. To optimally adapt such a framework to music signals, we also apply domain-specific modifications to model architecture, training scheme, and inference paradigm, with comprehensive ablation studies showing their effectiveness. Evaluations on the MARBLEv2 benchmark show that PupuM2D outperforms the sequence-based SSL models across multiple MIR tasks in linear probing. Additionally, case studies of the attention maps also confirm that PupuM2D captures musically meaningful patterns within the 2D time-frequency domain. Codes and checkpoints are available at: https://www.yichenggu.com/PupuM2D/.

We introduce PHAST-Net, an attention-guided, physics-informed network for unified estimation of Ideal Time-Frequency Representations (ITFRs), spanning spectral, tempo-based, metrical, and harmonic representations such as Spectrograms, Tempograms, and Metrograms. PHAST-Net learns an application-general mapping from a constellation of wavelet transforms, the proposed Continuous Log-frequency Adaptive Wavelet Transform (CLAWT), to high-resolution, cross-term-suppressed time-frequency (T-F) representations. The proposed constellation of CLAWTs is selected through Cohen's class kernel analysis to maximise curvature coverage in a logarithmic-frequency T-F plane tailored to harmonic signal structure. PHAST-Net further incorporates a proposed physics-informed auxiliary reprojection loss designed to reconstruct the idealised observed CLAWT constellation from the predicted ITFR and the corresponding Cohen's class kernels during training. This auxiliary objective promotes transform consistency and energy conservation, mitigates pathological target sparsity, and enhances optimisation stability. Attention layers further promote effective cross-term suppression across the input constellation. The log-frequency formulation also enables Harmonic PHAST-Net, which estimates a Harmonic ITFR that isolates fundamental structure, supporting robust fundamental-only representations for speech and music, such as derived fundamental Tempograms and Metrograms. We further introduce Spline-PHAST-Net, which parameterises detected and associated T-F ridges as continuous spline trajectories, enabling arbitrary-grid re-rendering and signal reconstruction. Trained on an effectively unbounded procedurally generated dataset, PHAST-Net demonstrates improved accuracy over established approaches, providing a unified framework for high-resolution, cross-term-robust analysis of speech, music, and broader nonstationary signals.

Conventional training losses for speech enhancement based on the signal-to-distortion ratio (SDR) treat all time-frequency (TF) regions uniformly, overlooking the fine-grained spectral cues that are relevant to specific phoneme intelligibility. We propose a TF weighting framework that modulates the SDR objective based on local speech presence, speech-to-interference ratio (SIR), and spectral flux. By integrating these factors into a differentiable objective, the framework emphasizes TF bins with high speech-noise competition while also accounting for transient cues such as consonant bursts. Experimental results show that our approach improves objective frequency-weighted enhancement metrics, as well as phoneme recognition accuracy, particularly for consonants. Spectral analysis shows better reconstruction of mid-frequency structures at less adverse SIR.

Medical time series (MedTS) signals such as electroencephalography (EEG) and electrocardiography (ECG) support many clinical applications. However, substantial subject-level heterogeneity often induces subject-level distribution shift, causing a fixed parameter set to generalize poorly to unseen individuals. Compared with domain adaptation methods that often depend on extra adaptation components or target-batch statistics, Test-Time Training (TTT) provides a more practical solution for sequential clinical data by enabling online adaptation from unlabeled test samples. However, many representative TTT methods require iterative inner-loop optimization, increasing test-time overhead. In this paper, we propose MedTS-TTT, a test-time training framework for medical time series modeling. MedTS-TTT is built upon Closed-Loop Self-Alignment Test-Time Training (CLSA-TTT) and a Gated Convolutional Backbone (GCB). CLSA-TTT constructs a token-level self-supervised target and performs a single-step fast-weight update for intra-layer closed-loop alignment, enabling rapid sample-wise adaptation without iterative inner-loop optimization. GCB combines CLSA-TTT-based fast adaptation and token-level fusion with a gated convolutional branch to balance local dynamic modeling and information-flow control. On 4 public datasets (2 EEG and 2 ECG) with subject-independent splits, MedTS-TTT achieves 11 top-1 rankings out of 12 evaluations across 9 baselines and 3 metrics. The code is publicly available at https://github.com/mingzhi-c/MedTS-TTT.

We study training-free fixed-length descriptors for multivariate time series and ask not merely whether such a descriptor performs well, but when it can be expected to work at all. Our object of study is $D(τ)$, built from a time-lagged correlation matrix truncated at the Marchenko-Pastur edge so that only signal-bearing eigenvalues survive and classified by cosine similarity to class centroids with zero learned parameters. The central contribution is not the descriptor but a falsifiable applicability criterion for it. Working from a stationary Gaussian VAR(1) model, we argue that $D(τ)$ separates two classes when the signals are approximately stationary and the class information lives in their cross-channel temporal coupling rather than in marginal per-channel power. We derive, semi-formally, three consequences: a distinguishability condition, why the static ($τ=0$) covariance collapses to chance, and why a stationary but power-discriminated paradigm defeats the descriptor. The criterion is operational: a two-part pre-flight test -- an augmented Dickey-Fuller stationarity check and a power-baseline saturation check -- predicts applicability before any training. We validate both halves on a mixed assortment. On four paradigms that satisfy the criterion (Sleep-EDF, BCI-IV-2a, MIT-BIH, ESC-50) the descriptor is competitive with strong baselines at a fraction of their cost, reaching $88.5\pm4.5\%$ under 20-subject leave-one-subject-out on Sleep-EDF on a single CPU thread. On three that violate it -- non-stationary ERPs, and financial-volatility and wearable-stress regimes that are power-discriminated -- it fails exactly as the pre-flight predicts, and these negatives are the more informative half. We are explicit that $D(τ)$ is not the most accurate representation; its value is a compact, training-free embedding whose domain of validity is known in advance.

Passive acoustic monitoring enables large-scale observation of wildlife, but most bioacoustic classifiers only predict species presence in a time window without localizing vocalizations precisely in time or frequency, limiting downstream analyses. We formulate bird vocalization detection as an object detection task on spectrograms and train YOLO11 models to localize bird calls in dense tropical soundscapes from Singapore. We additionally introduce an open-source browser-based annotation tool and propose Intersection over Minimum (IoMin), an evaluation metric that better handles ambiguous acoustic boundaries than standard IoU and is better suited to the problem at hand. The best YOLO model nearly doubles baseline performance on in-distribution soundscapes from Singapore (81.8% vs. 42.1% IoMin@50 F1-score) while still outperforming the baseline on unseen out-of-distribution recordings from Hawaii (58.6% vs. 48.6%). These results suggest that object detection frameworks are a promising approach to time-frequency localization of animal vocalizations in complex soundscapes.

A new fractional ambiguity function (NFrAF) derived from the fractional Fourier transform is introduced as a generalization of the classical ambiguity function. The fundamental analytical properties of the NFrAF, including symmetry, marginality, and Moyal type identities, are rigorously established. After verifying its ability to detect and localize monocomponent and multicomponent linear frequency modulated (LFM) signals, the NFrAF is integrated into a convolutional neural network based machine learning framework for signal classification. Owing to its superior time frequency resolution and localization, the NFrAF provides a more informative input representation than conventional methods such as the spectrogram and classical ambiguity function. Experimental results on simulated datasets demonstrate consistent improvements in classification accuracy, highlighting the effectiveness of the proposed representation for data driven signal analysis.

Out-of-distribution (OOD) detection for time-series data remains comparatively underexplored compared to vision and language, with a limited principled understanding of how supervised time-series representations can be leveraged for reliable detection under distributional shifts. This work formulates time-series OOD detection as representation learning with hyperspherical embeddings, where class-conditional structure is induced by a von Mises-Fisher (vMF) likelihood-based objective on the unit sphere. The learned representation combines time- and frequency-domain views of the input signal via domain-specific encoders, integrating them into a joint embedding space for OOD detection. Detection uses distance-based scores over the learned embeddings, including k-nearest neighbors (k-NN) and Mahalanobis scores. We evaluate the approach at scale on the complete UCR and UEA time-series archives under a cross-dataset protocol. Empirical results show consistent improvements under both k-NN and Mahalanobis scoring over strong contrastive learning and post-hoc baselines in the same setting. Code is available at https://github.com/tiiuae/hypertf-time-series-ood.

Electrocardiogram (ECG)-based biometric recognition has emerged as a promising solution for secure authentication and liveness detection. However, most existing methods rely on unimodal deep learning architectures that independently process either one-dimensional (1D) temporal signals or two-dimensional (2D) time-frequency representations, limiting robustness and generalization. To address this issue, this paper proposes a hybrid framework integrating 1D and 2D convolutional neural networks (CNNs) within a unified end-to-end architecture. The 1D branch extracts temporal and morphological features from raw ECG signals, while the 2D branch captures discriminative spectral information from time-frequency representations. An attention-guided fusion mechanism dynamically weights both modalities according to input characteristics, overcoming the limitations of conventional static fusion strategies. The framework was evaluated on three benchmark datasets (ECG-ID, MIT-BIH, and PTB), including healthy subjects and patients with cardiac pathologies, achieving identification accuracies of 99.56%, 100.00%, and 99.89%, respectively. To assess long-term biometric permanence, experiments were also conducted on the multi-session Heartprint dataset spanning ten years. The proposed approach achieved same-session accuracies of 98.54% (S1), 99.09% (S2), 94.93% (S3R), and 96.08% (S3L), while cross-session evaluations reached 56.33% (S1-S2) and 53.27% (S2-S3R), demonstrating the ability to capture stable biometric signatures over time. The optimal configuration combines InceptionTime for 1D processing, ResNet-34 for 2D analysis, and attention-based fusion. Ablation studies confirm that the proposed attention mechanism consistently outperforms conventional fusion approaches. Overall, the proposed framework provides a robust, scalable, and high-performance solution for ECG biometric recognition.

Autoregressive music generation depends strongly on the audio tokenizer. Existing high-fidelity codecs often use residual multi-codebook quantization, which preserves reconstruction quality but complicates language modeling after sequence flattening, as the residual hierarchy imposes strong sequential dependencies and can amplify error accumulation. We propose BandTok, a generation-oriented 2D Mel-spectrogram tokenizer that represents each frame with Mel-frequency band tokens from a single shared codebook. This design yields a physically interpretable time-frequency token grid with a more independent token structure, making it better suited for autoregressive modeling. BandTok improves reconstruction with a multi-scale PatchGAN objective and EMA codebook updates. We further introduce an autoregressive language model with 2D Rotary Position Embedding (2D RoPE) to preserve temporal and frequency-band structure during generation. Experiments show that BandTok improves over residual-codebook tokenizers and achieves strong results in a data-limited setting. The source code and generation demos for this work are publicly available.

The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks in which the neurons' states are governed by time-varying dynamics. The proposed model provides the learnable time-varying dynamics through a dictionary of basis functions, where each basis function evolves differently over time. We evaluate the proposed approach on both synthetic data from switching systems and a speech denoising task where real audio is corrupted with switching dynamics noise. The results show that the proposed time-varying model consistently outperforms its time-invariant counterparts while maintaining comparable computational complexity. Our investigations also reveal which aspects of the time-varying dynamics of the data most need to be captured by the proposed time-invariant models, how the additional freedom provided by time-varying basis functions should be allocated across model components, and to what extent larger models can compensate for time-invariant limitations.

Quantum machine learning has emerged as a promising tool for pattern recognition, yet many audio-focused approaches still treat spectrograms as generic images and do not explicitly exploit their time-frequency structure. We propose Q-Patch, a quantum feature map tailored to audio that encodes local time-frequency patches from mel-spectrograms into quantum states using shallow, hardware-efficient circuits with adjacency-aware entanglement. Each selected patch is summarized by a compact four-dimensional acoustic descriptor and mapped to a four-qubit circuit with depth at most three, enabling practical quantum kernel construction under near-term constraints. We evaluate Q-Patch on an audio spoofing detection task using a controlled, balanced protocol and compare it with size-matched classical baselines. Q-Patch improves discrimination between bona fide and spoofed samples, achieving an area under the receiver operating characteristic curve (AUROC) of 0.87, compared with 0.82 for a radial basis function support vector machine (RBF-SVM) trained on the same patch-level features. Kernel-space analysis further reveals a clear class structure, with cross-class similarity around 0.615 and within-class self-similarity of 1.00. Overall, Q-Patch provides a practical framework for incorporating time-frequency-aware representations into quantum kernel learning for audio authenticity assessment in low-resource settings.

Learning meaningful representations from medical time series (MedTS) such as ECG or EEG signals is a critical challenge. These signals are often high-dimensional, variable-length and rife with noise. Existing self-supervised approaches, such as Masked Autoencoders (MAEs) are highly effective for pre-training general-purpose encoders. However, they do not explicitly learn compact and semantically interpretable latent representations, typically relying on heuristic aggregation strategies such as global average pooling or a designated [CLS] token. We propose a novel framework that compresses a variable-length MedTS into a fixed-size set of $k$ latent Fingerprint Tokens. Our architecture employs a cross-attention bottleneck to generate these tokens and is trained with a dual-objective function. The first objective is a reconstruction loss, which ensures the tokens are \textit{sufficient statistics} for the original data. The second, a diversity penalty based on the Total Coding Rate (TCR), explicitly minimizes the redundancy between tokens, encouraging them to become statistically \textit{disentangled} representations. We present the theoretical justification for our method, framing it as a novel \textbf{Disentangled Rate-Distortion} problem. This approach produces a low-dimensional, interpretable, and sample-efficient representation, where each token is encouraged to capture an independent factor of variation, paving the way for more robust digital biomarkers.

In this paper, we propose a novel approach for generating music based on an artificial intelligence (AI) system. We analyze the features of music and use them to fit and predict the music. The fractional Fourier transform (FrFT) and the long short-term memory (LSTM) network are the foundations of our method. The FrFT method is used to extract the spectral features of a music piece, where the music signal is expressed on the time and frequency domains. The LSTM network is used to generate new music based on the extracted features, where we predict the music according to the hidden layer features and real-time inputs using GiantMIDI-Piano dataset. The results of our experiments show that our proposed system is capable of generating high-quality music that is comparable to human-generated music.

Systolic murmurs are extra heart sounds that occur during the contraction phase of the cardiac cycle, often indicating heart abnormalities caused by turbulent blood flow. Their intensity, pitch, and quality vary, requiring precise identification for the accurate diagnosis of cardiac disorders. This study presents an automatic classification system for systolic murmurs using a feature extraction module, followed by a classification model. The feature extraction module employs complex orthogonal matching pursuit to project single or multiple murmur segments onto a redundant dictionary composed of multiresolution complex Gabor basis functions (GBFs). The resulting projection weights are split and reshaped into variable-resolution time--frequency feature matrices. Processing multiple segments of a single recording using a shared dictionary mitigates murmur variability. This is achieved by learning the weights for each segment while enforcing that they correspond to the same set of basis functions in the dictionary, promoting consistent time--frequency feature matrices. The classification model is built based on a vision transformer to process multiple input matrices of different resolutions by passing each through a convolutional neural network for patch tokenization. All embedding tokens are then concatenated to form a matrix and forwarded to an encoder layer that includes multihead attention, residual connections, and a convolutional network with a kernel size of one. This integration of multiresolution feature extraction with transformer-based feature classification enhances the accuracy and reliability of heart murmur identification. An experimental analysis of four types of systolic murmurs from the CirCor DigiScope dataset demonstrates the effectiveness of the system, achieving a classification accuracy of $95.96\%$.

Time-frequency representations, such as the short-time Fourier transform (STFT), are fundamental tools for analyzing non-stationary signals. However, their ability to achieve sharp localization in both time and frequency is inherently limited by the Gabor-Heisenberg uncertainty principle. In this paper, we address this limitation by introducing a method to generate super-resolution spectrograms through the fusion of two or more spectrograms with varying resolutions. Specifically, we compute the super-resolution spectrogram as the barycenter of input spectrograms using optimal transport (OT) divergences. Unlike existing fusion approaches, our method does not require the input spectrograms to share the same time-frequency grid. Instead, the input spectrograms can be computed using any STFT parameters, and the resulting super-resolution spectrogram can be defined on an arbitrary user-specified grid. We explore various OT divergences based on different transportation costs. Notably, we introduce a novel transportation cost that preserves time-frequency geometry while significantly reducing computational complexity compared to standard Wasserstein barycenters. We adopt the unbalanced OT framework and derive a new block majorization-minimization algorithm for efficient barycenter computation. We validate the proposed method on controlled synthetic signals and recorded speech using both quantitative and qualitative evaluations. The results show that our approach combines the best localization properties of the input spectrograms and outperforms an unsupervised state-of-the-art fusion method.

This letter presents a CWT-enhanced vibration sensing framework for bearing fault monitoring through localized time-frequency region detection on continuous wavelet transform (CWT) spectrograms. Vibration signals are transformed into CWT spectrograms to improve the observability of weak and non-stationary fault signatures, and YOLOv9, YOLOv10, and YOLOv11 are employed to detect and identify localized fault-related energy regions in the time-frequency domain. Experiments on the CWRU, PU, and IMS datasets show that the proposed framework improves the detectability and robustness of fault-related sensing patterns compared with conventional time-series models, modern vision backbones, and short-time Fourier transform (STFT)-based representations, achieving mean average precision (mAP) values up to 99.4%, 97.8%, and 99.5%, respectively. In addition, the localized region detection framework provides a more interpretable relationship between time-frequency energy distributions and characteristic bearing fault frequencies. These results demonstrate an effective and generalizable approach for interpretable vibration sensing in noisy industrial environments.