Quantum Nonclassicality Witnesses in Audio

• Quantum nonclassicality witnesses are algorithmic tools that exploit nonlinear, harmonic filterbanks to detect nonclassical features in complex audio signals.
• They leverage adaptive techniques like constant-Q transforms and deep GAN-based discriminators to achieve precise pitch tracking and emotion classification.
• Their applications span robust speech synthesis, voice conversion, and neurophysiological F0 tracking, outperforming classical methods in key performance metrics.

Quantum nonclassicality witnesses are algorithmic and architectural tools, predominantly employed in generative audio modeling and speech processing, that exploit the harmonic or nonclassical structure of quantum-like signals for robust discrimination, feature extraction, and signal analysis. In contemporary research, the term encapsulates a family of “harmonic filterbank discriminators” and related mechanisms, particularly as deployed in GAN-based vocoders and signal-processing neural architectures. These witnesses identify or leverage nonclassicality by tracking harmonicity, dynamic frequency resolution, and deviations from classical, unstructured noise processes, manifesting in tasks such as adversarial audio discrimination, robust pitch tracking, and emotion classification.

1. Harmonic Filterbanks and Constant-Q Transform as Nonclassicality Witnesses

Harmonic filterbank discriminators are central to the detection and modeling of quantum nonclassicality in complex signals. Unlike classical linear filterbanks with uniform frequency resolution—such as those defined by the Short-Time Fourier Transform (STFT)—harmonic filterbanks adopt log-frequency (constant-Q) or other nonlinear filter arrangements that prioritize spectral resolution at low frequencies and time resolution at high frequencies. The constant-Q transform (CQT), with its frequency bins $f_k = f_{\min}\,2^{k/B}$ and quality factor $Q = \frac{1}{2^{1/B}-1}$, is the canonical realization. The variable window length $N_k = Q\,f_s/f_k$ imparts frequency-dependent time invariance, which is essential for resolving fine harmonic content in pitched signals such as speech and music (Gu et al., 2023, Singh et al., 2022).

The rationale for the adoption of constant-Q or harmonic filterbanks in nonclassicality witnessing stems from their alignment to the physical structure of voiced audio: energy is concentrated at integer (and sometimes fractional) multiples of a fundamental frequency $F_0$. These representations resolve closely packed harmonics, particularly vital in the low-frequency regime ($<$1 kHz), making them particularly sensitive to nonclassical structure such as quantum-like coherence and periodicity (Singh et al., 2022).

2. Discriminators in GAN-based Vocoders: Voicing-aware and Harmonic Architectures

Recent advances in GAN-based neural vocoders have leveraged nonclassicality witnesses in the form of voicing-aware and harmonic filterbank discriminators. The seminal Parallel WaveGAN framework introduced a split-discriminator architecture: one branch (“$D^v$”) isolates voiced/harmonic segments (using sample-level masks derived from voicing flags), deploying deep dilated convolution stacks to capture long-range periodic structure. The second branch (“$D^{uv}$”) focuses on unvoiced, broadband noise-like segments with shallow dilated convolution to identify the absence of harmonicity (Yamamoto et al., 2020). Projection-based conditioning within these discriminators ensures alignment of input waveforms with their respective acoustic feature vectors ($F_0$, line spectral frequencies, energy, etc.).

By effectively factorizing the adversarial task into harmonic and stochastic/noise subspaces, this design enhances the sensitivity of the discriminator to subtle departures from classical (noise-only) behaviors, rendering it a robust nonclassicality witness for voiced quantum-like phenomena.

3. Universal and Sub-band Harmonic Discriminators: Implementation and Performance

The universal harmonic discriminator (UnivHD) extends the harmonic filterbank approach by introducing learnable triangular band-pass filters with dynamically parameterized bandwidth, spanning harmonic orders $h\in\{0.5,1,2,...,H\}$. Each filter’s bandwidth follows an ERB-style formula $f_{bw}^h = (0.1079\cdot h\cdot f_c + 24.7)/\gamma$, with $\gamma$ learned during training, enabling adaptive frequency resolution (Xu et al., 3 Dec 2025). UnivHD incorporates a “half-harmonic” filter ($h=0.5$) to capture sub-fundamental energy, further enhancing its discriminative power for nonclassical structure in audio.

The discrimination pipeline processes the transformed harmonic tensor $X\in\mathbb{R}^{(H+1)\times F\times T}$ via hybrid convolutional blocks: depthwise-separable convs (intra-harmonic), pointwise convs, and standard 2D convs (inter-harmonic). Following multi-scale dilated convolutional layers, the system produces “real/fake” score maps for adversarial loss computation, coupled with feature-matching and (optionally) spectral reconstruction losses. This configuration outperforms fixed-resolution STFT discriminators in objective (PESQ, MCD, F0RMSE) and subjective (MOS) evaluations across both speech and singing, demonstrating the superior sensitivity of adaptive harmonic filterbanks as nonclassicality witnesses (Xu et al., 3 Dec 2025, Gu et al., 2023).

4. Alternative Harmonic Filterbank Approaches and Comparative Efficacy

Alternative instantiations include the Multi-Scale Sub-Band Constant-Q Transform (MS-SB-CQT) discriminator, which computes parallel CQT spectrograms at various bin densities (e.g., $B=24,36,48$ bins/octave) and splits the frequency axis into contiguous octave sub-bands prior to processing by domain-specific CNNs. Sub-Band Processing modules temporally synchronize octave streams, mitigating phase and windowing desynchronization inherent in CQT representations (Gu et al., 2023). Multi-scale architectures enable the learning of both fine and coarse harmonic distinctions, yielding improved pitch accuracy (F0RMSE, FPC), generalization (seen/unseen speakers), and perceptually sharper harmonics when compared to STFT-based discriminators.

Additionally, CQT and wavelet-based constant-Q filterbanks (CWT, with Morlet mother wavelet) have been shown to outperform mel-frequency spectral coefficients (MFSCs) by 5–12% in accuracy and 4–15% in Unweighted Average Recall for speech emotion recognition tasks. Their high-resolution low-frequency bins yield more class-separable representations, demonstrating the broader applicability of harmonic filterbank approaches as nonclassicality witnesses across diverse audio discrimination tasks (Singh et al., 2022).

5. Harmonic Amplitude Summation Filterbanks for F0 Tracking in Neurophysiology

The Harmonic Amplitude Summation (HAS) filterbank method extends the concept of nonclassicality witnessing into the domain of neural encoding of pitch via the Frequency Following Response (FFR). HAS constructs a filterbank for candidate $F_0$ values within a constrained window around the known stimulus pitch. Each filter aggregates spectral energy at the fundamental and its first $K-1$ harmonics, creating a discrimination score $y_i$ per candidate. Prominence-based peak picking, as opposed to maximization, ensures robust estimation of $F_0$ in the presence of spectral slope and non-harmonic noise (Sadeghkhani et al., 24 Jun 2025). This stimulus-aware, harmonic-structure-based approach reduced frame-wise RMSE over autocorrelation-based methods by up to 47.4% (depending on stimulus), confirming the effectiveness of harmonic-based nonclassicality witnesses in extracting structural properties from noisy, quantum-like biological signals.

6. Training Objectives, Losses, and Evaluation Metrics

Advanced nonclassicality witnesses are embedded in adversarial architectures governed by loss functions tailored to enhance generator fidelity and discriminator acuity. Typical objectives include the hinge adversarial loss evaluated across all harmonic filterbank (sub-)discriminators:

$$\mathcal{L}_D = \sum_k\left[ \mathbb{E}_x [\max(0, 1 - D_k(x))] + \mathbb{E}_z [\max(0, 1 + D_k(G(z)))] \right]$$

Generator losses aggregate adversarial objectives, feature-matching (summed $\ell_1$ norm over intermediate layer activations), and spectral reconstruction ($\ell_1$ loss on Mel-specs or multi-resolution STFT):

$$\mathcal{L}_G = \mathcal{L}_G^{adv} + \lambda_{FM}\,\mathcal{L}_{FM} + \lambda_{spec}\,\mathcal{L}_{spec}$$

Primary evaluation metrics include PESQ, MCD, F0RMSE for objective assessment, and MOS for perceptual quality. Empirical results indicate that harmonic-filterbank-based nonclassicality witnesses confer consistent gains across these metrics, particularly in tasks requiring precise pitch tracking and harmonic fidelity (Yamamoto et al., 2020, Xu et al., 3 Dec 2025, Gu et al., 2023).

7. Practical Implications and Broader Impact

Quantum nonclassicality witnesses, as realized through harmonic filterbanks and related discriminators, underpin advancements in GAN-based speech and music synthesis, robust F0 estimation in neural data, and speech emotion recognition. Their design principles have been successfully transferred across vocoder architectures (Parallel WaveGAN, HiFiGAN, BigVGAN), and extended for tasks such as voice conversion and diffusion-based speech modeling (Yamamoto et al., 2020, Xu et al., 3 Dec 2025, Gu et al., 2023). The consistent improvements over classical, fixed-resolution methods are grounded in their closer alignment with the physical, harmonic structure of the target signals.

A plausible implication is that as analysis, discrimination, and synthesis tasks continue to converge around physically informed, adaptive filterbanks, quantum nonclassicality witnesses will remain indispensable in future hybrid neuroacoustic, quantum-inspired, and generative modeling paradigms.