Compressed identification by sparse sampled frequency data

This paper considers the identification of a rational transfer function with sparse representation in pairs of FIR and Takenaka-Malmquist (TM) bases and from random sampled linear frequency-domain measurements. We firstly prove the uniqueness of the sparse representation of the transfer function represented in concatenated FIR and TM basis functions. Then we propose to reconstruct the unique representation coefficient vector by ℓ
₁
minimization with sparse sampled frequency data on the upper unit circle. The simulations verify that the concatenated FIR and TM bases in the proposed identification framework can obtain a much sparser reconstruction with lower reconstruction order even with incomplete information of the system poles.