Proof of Hermitian Self-Adjoint Product Identity for Equidistant Time-Domain Measurements

Authors: (1) Michael Sorochan Armstrong, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (2) Jose Carlos P´erez-Gir´on, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada; (3) Jos´e Camacho, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (4) Regino Zamora, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada. Table of Links Abstract & Introduction Optimization of the Optical Interpolation Materials and Methods Results and Discussion Conclusion Appendix A: Proof of Hermitian Self-Adjoint product identity for Equidistant Time-Domain Measurements Appendix B: AAH ̸= MIN I in the Non-Equidistant Case Acknowledgments & References APPENDIX A: PROOF OF HERMITIAN SELF-ADJOINT PRODUCT IDENTITY FOR EQUIDISTANT TIME-DOMAIN MEASUREMENTS Consider the case of an NFFT matrix and its hermitian, where: Equation 44 simplifies to: This paper is available on arxiv under CC 4.0 license. Authors: (1) Michael Sorochan Armstrong, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (2) Jose Carlos P´erez-Gir´on, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada; (3) Jos´e Camacho, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (4) Regino Zamora, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada. Authors: Authors: (1) Michael Sorochan Armstrong, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (2) Jose Carlos P´erez-Gir´on, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada; (3) Jos´e Camacho, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (4) Regino Zamora, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada. Table of Links Abstract & Introduction Abstract & Introduction Optimization of the Optical Interpolation Optimization of the Optical Interpolation Materials and Methods Materials and Methods Results and Discussion Results and Discussion Conclusion Conclusion Appendix A: Proof of Hermitian Self-Adjoint product identity for Equidistant Time-Domain Measurements Appendix A: Proof of Hermitian Self-Adjoint product identity for Equidistant Time-Domain Measurements Appendix B: AAH ̸= MIN I in the Non-Equidistant Case Appendix B: AAH ̸= MIN I in the Non-Equidistant Case Acknowledgments & References Acknowledgments & References APPENDIX A: PROOF OF HERMITIAN SELF-ADJOINT PRODUCT IDENTITY FOR EQUIDISTANT TIME-DOMAIN MEASUREMENTS Consider the case of an NFFT matrix and its hermitian, where: Equation 44 simplifies to: This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv