Stochastic signal representation via harmonic parameter factorization

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.