TITLE:
Continuous-Time and Discrete-Time Singular Value Decomposition of an Impulse Response Function
AUTHORS:
Rogelio Luck, Yucheng Liu
KEYWORDS:
Singular Value Decomposition, Impulse Response Function, Green’s Function, Toeplitz Matrix, Hankel Matrix
JOURNAL NAME:
Applied Mathematics,
Vol.12 No.4,
April
28,
2021
ABSTRACT: 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.