Spectral Estimation (line spectrum / parametric PSD) L1-394
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
A complex-exponential / sinusoidal signal is modeled as sum of K components with unknown frequencies omega_k, amplitudes c_k, and phases phi_k, observed on a finite time window of N samples plus noise; the goal is to estimate (omega_k, c_k, phi_k) via subspace, parametric, or atomic-norm methods.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- for well-separated frequencies (delta_omega > 4pi/N) — Rayleigh criterion
- Stability:
- conditional
- κ:
- 500
Fourier-limited resolution 2pi/N; subspace methods (MUSIC, ESPRIT) achieve super-resolution given SNR; atomic-norm minimization (Tang-Bhaskar-Shah-Recht) guarantees exact recovery when delta_omega > 4pi/N.
Solvability C
- Solver class:
- Periodogram/Welch, Yule-Walker AR, MUSIC, ESPRIT, Prony, atomic-norm (AST), sparse BPDN in DFT grid, Nonlinear LS
- Convergence rate q:
- 2
- Complexity:
- FFT: O(N*log(N)); MUSIC O(N^3 + N^2*Ngrid); ESPRIT closed-form; atomic SDP O(N^3.5)