Frequency domain subspace-based identification of discrete-time power spectra from nonuniformly spaced measurements

Subspace-based rational interpolation of analytic functions from real or imaginary parts of frequency-response data

“…This splitting of S(z) into the sum of a causal transfer function ψ(z) and an anti-causal transfer function ψ(z −1 ) is the first step of the subspace-based identification algorithms in [8], [4]. The transfer functions ψ(z) and ψ(z −1 ) are called the spectral summands of S(z).…”

“…(The case that f (z) is a positive-real transfer function can be handled similarly to the spectral estimation problem). In [4], the interpolation condition, which links the number of data with the system order, is derived in Lemma 2 there. This condition is obtained under the assumption that the realization (A, β , 2c, γ/2) is minimal, which is equivalent to the minimality of (A, b, 2c, d).…”

“…Since the positivity of the spectrum is enforced after the estimation of the spectral summands, the consistency properties carry on to the next stages of the algorithms in [8], [4]. Moreover, the interpolation properties of these algorithms are determined in the estimation step of ψ(z) from the spectrum samples.…”

“…The transfer functions ψ(z) and ψ(z −1 ) are called the spectral summands of S(z). In [8], [4], realizations similar to (A, β , 2c, γ 2 ) are consistently estimated from corrupted power spectrum samples S k . The subspace-based algorithms proposed in [8], [4] do not require the power spectrum be scalar-valued.…”

“…The objective of this paper is to show that the algorithm in [4], which identifies discrete-time power spectra from non-uniformly spaced measurements, can be used to solve the problem considered in this paper. The reader is referred to the works [4], [5], [6], [7], [8], [9] and the references therein for the motivation and the derivations of frequency-domain subspace-based identification algorithms.…”