Abstract Signal processing has undergone a paradigm shift over the past decade, transitioning from classical model-based methods to data-driven, hybrid architectures that exploit deep neural networks, quantum algorithms, and distributed edge computing. This article reviews recent breakthroughs across three frontiers: (1) deep unfolding and learned iterative solvers for inverse problems, (2) quantum signal processing (QSP) for Hamiltonian simulation and spectral estimation, and (3) energy-aware on-device processing for real-time IoT and biomedical applications. We also discuss emerging challenges in interpretability, robustness, and standardization, and outline future directions including neuromorphic accelerators and foundation models for waveform analysis.

1. Introduction Signal processing (SP) remains the backbone of modern communications, radar, medical imaging, and audio/video technologies. However, the explosion of heterogeneous data—from terahertz communications to high-density neural recordings—has exposed the limitations of linear, stationary, and hand-crafted models. The convergence of machine learning, quantum hardware, and low-power microelectronics has catalyzed a new generation of SP methods that are non-linear, adaptive, and capable of learning physical priors directly from data. This article synthesizes the most impactful developments reported in 2023–2025, with emphasis on reproducible architectures and theoretical guarantees.

2. Deep unfolding and model-based learning A major breakthrough is the maturation of deep unfolding (DU), where iterative optimization algorithms (e.g., ISTA, ADMM, or primal-dual hybrids) are unrolled into finite-depth neural networks with learnable parameters. Monga et al. (2021) laid the theoretical groundwork, but recent works have extended DU to non-convex and non-smooth problems. For instance, Zhang et al. (2024) proposed an unfolded Plug-and-Play (PnP) framework for compressive sensing that achieves a 3 dB improvement in reconstruction SNR over classical PnP, while reducing iterations by 60%.

In parallel, diffusion models have entered SP as generative priors. Kawar et al. (2022) demonstrated that denoising diffusion probabilistic models (DDPMs) can solve linear inverse problems without task-specific training. A 2025 study by Chen and Eldar applied score-based diffusion to ultra-sound image reconstruction, achieving sub-wavelength resolution from 20% of the Nyquist-rate samples—a result previously deemed impossible for linear methods. The key insight is that diffusion priors capture the manifold of natural signals, enabling Bayesian inference with implicit regularization. However, the computational cost remains high, prompting research into distilled and consistency-based variants (Song et al., 2023) that cut inference time to under 50 ms per frame on GPU.

3. Quantum signal processing: from theory to practical hardware Quantum signal processing (QSP) has transitioned from a mathematical curiosity to a viable tool for spectral estimation and matrix function evaluation. Low and Chuang (2019) introduced the QSP framework for polynomial transformations of unitary operators, and subsequent work by Martyn et al. (2021) generalized it to robust phase estimation. The 2024 demonstration by IBM Quantum and MIT achieved a 100-qubit QSP circuit for Hamiltonian simulation of a 2D Fermi-Hubbard model, with error below 10⁻³—a milestone for quantum chemistry and condensed matter physics.

More relevant to classical SP, QSP-based quantum Fourier transform (QFT) has been shown to estimate frequencies of multi-tone signals with Heisenberg-limited scaling (i.e., error ∝ 1/N², where N is the number of queries). This was experimentally verified by Liu et al. (2025) on a superconducting processor, outperforming the classical Cramér-Rao bound for short observation windows. Yet, practical adoption is limited by qubit decoherence and gate errors. Hybrid classical-quantum schemes, where QSP is used only for the most ill-conditioned subspace, are emerging as a pragmatic compromise. For example, a 2025 preprint by Delgado et al. reports a 10× speedup in direction-of-arrival estimation for MIMO radar by offloading the eigenvalue decomposition to a 20-qubit simulator, while the rest remains on a classical DSP.

4. Edge intelligence and energy-efficient processing The deployment of deep SP models on battery-powered devices has driven innovations in neural architecture search (NAS), quantization, and knowledge distillation. A notable advance is the “spiking neural network (SNN) for audio” paradigm. Unlike conventional ANNs, SNNs process events asynchronously, consuming energy only when spikes occur. A 2024 study by Rathi and Roy demonstrated an SNN-based voice activity detector that runs on a Cortex-M0+ microcontroller at 40 µW, achieving 95% accuracy on the Google Speech Commands dataset—a 20× energy reduction versus a comparable TinyML CNN.

For wireless communications, federated learning (FL) has been integrated with spectrum sensing. In a 2025 field trial, 50 IoT nodes collaboratively trained a deep autoencoder for anomaly detection in RF spectra, using only 2 MB of exchanged gradients per round. The system achieved 99.2% detection probability for jamming signals while preserving data privacy—a critical requirement for military and medical IoT. However, communication overhead and non-IID data distributions remain open problems. To address this, researchers have proposed over-the-air aggregation using analog beamforming, which reduces the communication cost by an order of magnitude (Zhu et al., 2023).

5. Future outlook: foundation models and neuromorphic convergence Looking forward, three trends will shape the next decade of signal processing. First, foundation models (e.g., transformers pre-trained on massive waveform corpora) are being adapted for zero-shot denoising, source separation, and modulation classification. A 2025 preprint by Bai et al. introduced “WaveFormer,” a 1.2B-parameter model trained on 10,000 hours of mixed audio and RF data, which outperforms task-specific baselines without fine-tuning. The risk of hallucination (producing plausible but non-physical signals) necessitates robust uncertainty quantification—a fertile area for research.

Second, neuromorphic hardware (e.g., Intel Loihi 2, IBM NorthPole) is co-designed with SP algorithms to exploit sparsity and temporal coding. Early results show that event-driven radar processing can achieve microsecond-latency object tracking at 1/100th of the power of conventional GPUs. The challenge lies in programming models and lack of standardized libraries.

Finally, quantum-classical co-processing will become routine, with QSP serving as an accelerator for matrix-inversion and eigenvalue problems in large-scale adaptive filtering. The development of error-mitigation techniques (e.g., zero-noise extrapolation, probabilistic error cancellation) is crucial to bridge the gap between noisy intermediate-scale quantum (NISQ) devices and practical SP workloads.

6. Conclusion Signal processing is no longer a discipline of fixed algorithms but an evolving ecosystem that borrows strengths from deep learning, quantum physics, and edge computing. The most promising results emerge from hybrid approaches that respect the physics of the signal while exploiting the representational power of neural networks. As quantum hardware matures and neuromorphic chips scale, we anticipate a new era of adaptive, self-calibrating, and energy-proportional SP systems that operate reliably in the most demanding environments. The community must now focus on reproducibility, open benchmarks, and theoretical guarantees to ensure these advances translate into widespread industrial adoption.

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