2012/03/08 by Manuel Servı́n, Servin, Manuel, Adonai Gonzalez +1
Computer Science · Engineering · #Advanced Adaptive Filtering Techniques #Advanced Fiber Optic Sensors #Blind Source Separation Techniques #Control Systems and Identification #FOS: Physical sciences #Optical measurement and interference techniques #Optics (physics.optics) #Structural Health Monitoring Techniques
paper · pdf · doi:10.48550/arxiv.1203.1947
openalex publication_date 2012/03/08 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28
We analyze the nonlinear Carr 'e 4-steps algorithm including its frequency\nresponse, signal-to-noise ratio, and harmonics rejection using linear systems\ntheory. At first sight the previous statement as well as the title of this\npaper seems paradoxical. How can we analyze the 4-step non-linear Carr 'e Phase\nShifting Algorithm (PSA) using linear system theory? The short answer is that\nthe non-linear Carr 'e algorithm may be decomposed into two building blocks.\nThe first block is a tunable linear 4-step PSA, and the second one is a\nnon-linear phase-step estimator. Although this fact is well known from the\nderivation of the Carr 'e algorithm, nobody has properly exploited it. In other\nwords, to this day, we do not have explicit mathematical formulae for a) the\nspectrum, b) the harmonics rejection, and c) the signal-to-noise ratio of the\nnon-linear Carr 'e algorithm. These are the properties of the Carr 'e's PSA\nthat we show here with novel and explicit mathematical formulae.\n