## A method for system identification with random inputs |

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and/or arbitrary basis autocorrelation function basis choices basis elements causal system coefficient measuring coefficients of h(t column vector contour integration convolution integral equation correlation functions cross-correlation Denote deterministic input deterministic problem deterministic system identification Fourier coefficients Fourier series functions f(t Gram-Schmidt process H(ja half plane pole identification of H(p impulse response h(T infinite matrix equation inner product input x(t integrand Jordan's lemma method for system number of elements orthogonal filters orthonormal basis orthonormal set parameters physically realizable pole locations pole positions poles per half positions in S^p proposed identification scheme random input problem rational function real exponentials reference to Figure residue evaluation respect result occurs right-half plane poles right-half plane zeros Rw(t RXX(T series expansion special basis stationary random input Sxx(p system identification problem system quiescent prior transform of R^t unitary transformation unknown impulse response zero of H(p zero vector