Acoustic Beamforming in the Presence of Finite Sample Size Estimates and Sampling Offsets / Tobias Gburrek ; Erster Gutachter: Prof. Dr.-Ing. Reinhold Häb-Umbach, Zweiter Gutachter: Prof. Dr.-Ing. Sharon Gannot. Paderborn, 2026
Inhalt
- Abstract
- Zusammenfassung
- Acknowledgments
- Introduction
- Prerequisites
- Signal model
- Asynchronous sampling
- Minimum variance distortionless response beamforming
- Wishart distribution
- Experimental setup for the analysis of MVDR beamforming
- Analysis of finite sample size effects on block-wise MVDR beamforming
- Modeling assumptions
- Statistical model of the beamformer coefficients
- Statistical model of the interference-SCM estimates
- First- and second-order moment of the beamformer coefficients
- Derivation of a closed-form approximation of the output SDR
- Analysis of the closed-form approximation of the output SDR
- Convergence behavior
- SCM estimation from oracle-separated signals
- Influence of the leakage of the target signal into the interference-SCM estimate
- Summary
- Evaluation
- Summary
- MVDR beamforming using asynchronous, distributed devices
- Compact microphone array vs. distributed recording devices for meeting recognition
- Impact of STOs on MVDR beamforming
- Impact of SROs on MVDR beamforming
- Summary
- Interplay of SCM estimation from a finite sample size and asynchronous sampling
- Derivation of a closed-form approximation of the output SDR in the presence of STOs
- Evaluation of the interplay of SCM estimation from a finite sample size and STOs
- Derivation of a closed-form approximation of the output SDR in the presence of SROs
- Evaluation of the interplay of SCM estimation from a finite sample size and SROs
- Summary
- Signal synchronization
- Compensation for STOs
- Compensation for SROs
- Existing SRO estimators
- Development of an SRO estimator for time-varying SROs in the presence of speaker position changes
- Evaluation
- Summary
- Summary and future work
- Appendix
- Derivation of the variance of the elements of a Wishart matrix
- Derivation of the variance of the elements of an SCM estimate
- Convergence of the off-diagonal elements of the SCM estimates
- Reformulation of the beamformer output for time frames that are dominated by a single source
- Expected value of the denominator accounting for the statistical dependence of the beamformer coefficients and the signals
- Matrix algebra
- Denominator of the signal power at the beamformer output in the presence of STOs
- Denominator of the signal power at the beamformer output in the presence of SROs
- Symbols and notation
- List of figures
- List of tables
- Acronyms
- Bibliography