Author(s)

Rogelio Luck, Yucheng Liu

Department of Mechanical Engineering, Mississippi State University, Mississippi State, MS, USA.

This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Singular Value Decomposition, Impulse Response Function, Green’s Function, Toeplitz Matrix, Hankel Matrix

Luck, R. and Liu, Y. (2021) Continuous-Time and Discrete-Time Singular Value Decomposition of an Impulse Response Function. Applied Mathematics, 12, 336-347. doi: 10.4236/am.2021.124024.