arXiv subjects

Christopher K. Kovach

Publications and source records attributed to Christopher K. Kovach.

6 recordsLinked to original sources

arXiv2026

Modulation Analysis with Higher-Order Spectra

A need to identify modulation of spectral power arises frequently in the analysis of physiological signals. Estimation of power in the relevant bands through filtering and envelope extraction has several limitations: the choice of filter may bias any resulting estimate, while additive Gaussian noise becomes non-Gaussian due to the nonlinearity of envelope computation. The present work considers how spectral decompositions of higher-order cumulants (higher-order spectra, HOS) avoid these limitations, with an emphasis on the use of the trispectrum to identify modulated oscillations. Specifically, it is shown: 1) The trispectrum may be interpreted as a measure of linear dependencies of power across frequencies by viewing it as the cross spectrum of the Wigner-Ville distribution. 2) A particular two-dimensional subdomain of the trispectrum is useful for identifying modulated carriers, recovering essential spectral properties of both the modulating and carrier signals while avoiding the cubic complexity of full trispectrum estimation. A representation of this subdomain, the modulogram, is demonstrated as a tool for identifying and distinguishing different forms of modulation. 3) As a cumulant-derived measure, the modulogram is not biased by additive Gaussian noise. 4) Modulogram phase retains information by which temporal patterns of modulation may be identified. 5) A recently described additive decomposition of HOS (HOSD) further aids identification when applied to the trispectrum. These developments are illustrated with the blind detection of beta bursts in rodent and human local field potential recordings. Finally, the relationship between the present approach and prior techniques of blind identification (BI) through moment maximization, including blind deconvolution and independent component analysis, is considered.

eess.SP↗

arXiv2025

Efficient Coherence Inference Using the Demodulated Band Transform and a Generalized Linear Model

Statistical significance testing of neural coherence is essential for distinguishing genuine cross-signal coupling from spurious correlations. A widely accepted approach uses surrogate-based inference, where null distributions are generated via time-shift or phase-randomization procedures. While effective, these methods are computationally expensive and yield discrete p-values that can be unstable near decision thresholds, limiting scalability to large EEG/iEEG datasets. We introduce and validate a parametric alternative based on a generalized linear model (GLM) applied to complex-valued time--frequency coefficients (e.g., from DBT or STFT), using a likelihood-ratio test. Using real respiration belt traces as a driver and simulated neural signals contaminated with broadband Gaussian noise, we perform dense sweeps of ground-truth coherence and compare GLM-based inference against time-shift/phase-randomized surrogate testing under matched conditions. GLM achieved comparable or superior sensitivity while producing continuous, stable p-values and a substantial computational advantage. At 80% detection power, GLM detects at C=0.25, whereas surrogate testing requires C=0.49, corresponding to an approximately 6--7 dB SNR improvement. Runtime benchmarking showed GLM to be nearly 200x faster than surrogate approaches. These results establish GLM-based inference on complex time--frequency coefficients as a robust, scalable alternative to surrogate testing, enabling efficient analysis of large EEG/iEEG datasets across channels, frequencies, and participants.

eess.SP↗

arXiv2019

Decomposition of Higher-Order Spectra for Blind Multiple-Input Deconvolution, Pattern Identification and Separation

Like the ordinary power spectrum, higher-order spectra (HOS) describe signal properties that are invariant under translations in time. Unlike the power spectrum, HOS retain phase information from which details of the signal waveform can be recovered. Here we consider the problem of identifying multiple unknown transient waveforms which recur within an ensemble of records at mutually random delays. We develop a new technique for recovering filters from HOS whose performance in waveform detection approaches that of an optimal matched filter, requiring no prior information about the waveforms. Unlike previous techniques of signal identification through HOS, the method applies equally well to signals with deterministic and non-deterministic HOS. In the non-deterministic case, it yields an additive decomposition, introducing a new approach to the separation of component processes within non-Gaussian signals having non-deterministic higher moments. We show a close relationship to minimum-entropy blind deconvolution (MED), which the present technique improves upon by avoiding the need for numerical optimization, while requiring only numerically stable operations of time shift, element-wise multiplication and averaging, making it particularly suited for real-time applications. The application of HOS decomposition to real-world signals is demonstrated with blind denoising, detection and classification of normal and abnormal heartbeats in electrocardiograms.

eess.SP↗

arXiv2018

The Bispectrum and Its Relationship to Phase-Amplitude Coupling

Most biological signals are non-Gaussian, reflecting their origins in highly nonlinear physiological systems. A versatile set of techniques for studying non-Gaussian signals relies on the spectral representations of higher moments, known as polyspectra, which describe forms of cross-frequency dependence that do not arise in time-invariant Gaussian signals. The most commonly used of these employ the bispectrum. Recently, other measures of cross-frequency dependence have drawn interest in EEG literature, in particular those which address phase-amplitude coupling (PAC). Here we demonstrate a close relationship between the bispectrum and popular measures of PAC, which we relate to smoothings of the signal bispectrum, making them fundamentally bispectral estimators. Viewed this way, however, conventional PAC measures exhibit some unfavorable qualities, including poor bias properties, lack of correct symmetry and artificial constraints on the spectral range and resolution of the estimate. Moreover, information obscured by smoothing in measures of PAC, but preserved in standard bispectral estimators, may be critical for distinguishing nested oscillations from transient signal features and other non-oscillatory causes of "spurious" PAC. We propose guidelines for gauging the nature and origin of cross-frequency coupling with bispectral statistics. Beyond clarifying the relationship between PAC and the bispectrum, the present work lays out a general framework for the interpretation of the bispectrum, which extends to other higher-order spectra. In particular, this framework holds promise for the detailed identification of signal features related to both nested oscillations and transient phenomena. We conclude with a discussion of some broader theoretical implications of this framework and highlight promising directions for future development.

stat.ME↗

arXiv2017

A Biased Look at Phase Locking: Brief Critical Review and Proposed Remedy

A number of popular measures of dependence between pairs of band-limited signals rely on analytic phase. A common misconception is that the dependence revealed by these measures must be specific to the spectral range of the filtered input signals. Implicitly or explicitly, obtaining analytic phase involves normalizing the signal by its own envelope, which is a nonlinear operation that introduces broad spectral leakage. We review how this generates bias and complicates the interpretation of commonly used measures of phase locking. A specific example of this effect may create spurious phase locking as a consequence of nonzero circular mean in the phase of input signals, which can be viewed as spectral leakage to 0 Hz. Corrections for this problem which recenter or uniformize the distribution of phase may fail when the amplitudes of the compared signals are correlated. To address the more general problem of spectral bias, a novel measure of phase locking is proposed, the amplitude-weighted phase locking value (awPLV). This measure is closely related to coherence, but it removes ambiguities of interpretation that detract from the latter.

q-bio.NC↗

arXiv2016

The demodulated band transform

Background: Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent application in electrophysiological research, including the short-time Fourier transform, continuous wavelets, band-pass filtering and multitaper-based approaches, each carries certain drawbacks related to computational efficiency and spectral leakage. This work surveys the advantages of a WFD not previously applied in electrophysiological settings. New Methods: A computationally efficient form of complex demodulation, the demodulated band transform (DBT), is described. Results: DBT is shown to provide an efficient approach to spectral estimation with minimal susceptibility to spectral leakage. In addition, it lends itself well to adaptive filtering of non-stationary narrowband noise. Comparison with existing methods: A detailed comparison with alternative WFDs is offered, with an emphasis on the relationship between DBT and Thomson's multitaper. DBT is shown to perform favorably in combining computational efficiency with minimal introduction of spectral leakage. Conclusion: DBT is ideally suited to efficient estimation of both stationary and non-stationary spectral and cross-spectral statistics with minimal susceptibility to spectral leakage. These qualities are broadly desirable in many settings.

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