Stochastic signal representation via harmonic parameter factorization

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. 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 cos ⁡ ϕ k , ⁡ sin ⁡ ϕ k , 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. 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. 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.