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Register a new userModal Analysis Using Sparse and Co-prime Arrays
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Added by
Ali Pezeshki
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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Let a measurement consist of a linear combination of damped complex exponential modes, plus noise. The problem is to estimate the parameters of these modes, as in line spectrum estimation, vibration analysis, speech processing, system identification, and direction of arrival estimation. Our results differ from standard results of modal analysis to the extent that we consider sparse and co-prime samplings in space, or equivalently sparse and co-prime samplings in time. Our main result is a characterization of the orthogonal subspace. This is the subspace that is orthogonal to the signal subspace spanned by the columns of the generalized Vandermonde matrix of modes in sparse or co-prime arrays. This characterization is derived in a form that allows us to adapt modern methods of linear prediction and approximate least squares, such as iterative quadratic maximum likelihood (IQML), for estimating mode parameters. Several numerical examples are presented to demonstrate the validity of the proposed modal estimation methods, and to compare the fidelity of modal estimation with sparse and co-prime arrays, versus SNR. Our calculations of Cram{e}r-Rao bounds allow us to analyze the loss in performance sustained by sparse and co-prime arrays that are compressions of uniform linear arrays.
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We present a new concept of an integrated optics component capable of measuring the complex amplitudes of the modes at the tip of a multimode waveguide. The device uses a photonic lantern to split the optical power carried by an $N$-modes waveguide among a collection of single-mode waveguides that excite a periodic array of at least $N^2$ single-mode evanescently-coupled waveguides. The power detected at each output of the array is a linear combination of the products of the modal amplitudes-a relation that can, under suitable conditions, be inverted allowing the derivation of the amplitudes and relative phases of the modal mixture at the input. The expected performance of the device is discussed and its application to the real-time measurement of modal instability in high power fiber lasers is proposed.
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