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2026
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Stochastic signal representation via harmonic parameter factorization
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Abstract
Introduction Stochastic waveforms are intrinsic to many physical and telecommunication processes, yet reproducible interfaces for converting them into compact stochastic representations suitable for bitstream-domain processing remain limited. Methods We represent each finite analysis window by a small set of dominant harmonic components and encode the interpretable parameters of each component-amplitude, frequency, and phase represented by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"> <mml:mrow> <mml:mfenced open="(" close=")" separators="|"> <mml:mrow> <mml:mi mathvariant="italic">cos</mml:mi> <mml:mo></mml:mo> <mml:msub> <mml:mi>ϕ</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mo></mml:mo> <mml:mi mathvariant="italic">sin</mml:mi> <mml:mo></mml:mo> <mml:msub> <mml:mi>ϕ</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> , with polarization as an optional extension-into calibrated Bernoulli bitstreams. Validation is performed using a NOT-NOT identity protocol that separates finite-K representational loss from finite-N stochastic encoding error. Results The method provides a compact and reproducible stochastic representation of noisy waveforms and enables transparent fidelity assessment through reconstruction error and process-level statistics, including power spectral density, autocorrelation, and amplitude distributions. The framework also supports direct comparison between truncation-limited and encoding-limited error sources. Discussion Harmonic parameter factorization offers an interpretable bridge between waveform-domain stochastic signals and probability/bitstream-domain processing, supporting controlled validation and reproducible downstream stochastic signal processing.
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