References: Spectral Estimation, Signal Processing, and Quantum Computing
17 May 2025
A list of key academic references in spectral estimation, signal processing techniques like Fourier analysis and super-resolution, and related applications
Lower Bound for Spectral Estimation in Noisy Super-Resolution
17 May 2025
This section presents the theoretical lower bound on the error for estimating locations and intensities in spectral estimation
Eigenvector Perturbation in Aligning Matrix Construction for ESPRIT
17 May 2025
Learn how the eigenvector perturbation lemma is used in the proof for constructing the crucial aligning matrix P in our analysis of the ESPRIT algorithm.
Explicit Expansion and Bounds of Spectral Projector in ESPRIT Analysis
16 May 2025
This section details the explicit formulas for higher-order terms in the perturbation expansion of the spectral projector, along with their bounds
Proofs of Central Limit Error Scaling Lemmas for ESPRIT
15 May 2025
This section provides the detailed proofs of Lemmas 2.1 and 2.2, which establish the central limit error scaling for the ESPRIT algorithm in spectral estimation
Vandermonde Matrices in Spectral Estimation Analysis
15 May 2025
This section discusses the crucial role of Vandermonde matrices in the analysis of spectral estimation algorithms, including Moitra's singular value bounds.
Mathematical Notations for Spectral Estimation Analysis
15 May 2025
Understand the key mathematical notations, symbols, and definitions used in our analysis of spectral estimation algorithms and related theories.
ESPRIT Algorithm: The Proof of Theorem
14 May 2025
Explaining the proof of theorem for our ESPRIT Algorithm academic paper.
Error Cancellation in the Taylor Expansion: The Details You Need to Know
14 May 2025
Here are the details of the error cancellation in the Taylor expansion.