Time-frequency transfer function calculus (symbolic calculus) of linear time-varying systems (linear operators) based on a generalized underspread theory

1998 ◽  
Vol 39 (8) ◽  
pp. 4041-4070 ◽  
Author(s):  
Gerald Matz ◽  
Franz Hlawatsch
Keyword(s):  
Transfer Function ◽  
Linear Time ◽  
Linear Operators ◽  
Symbolic Calculus ◽  
Time Varying ◽  
Time Frequency ◽  
Time Varying Systems ◽  
Frequency Transfer ◽  
Function Calculus

Biorthogonal Wavelet Based Identification of Fast Linear Time-Varying Systems—Part I: System Representations12

2000 ◽  
Vol 123 (4) ◽  
pp. 585-592 ◽  
Author(s):  
Haipeng Zhao ◽  
Joseph Bentsman
Keyword(s):  
Banach Space ◽  
Discrete Time ◽  
Linear Time ◽  
Block Diagram ◽  
Approximation Problem ◽  
Time Varying ◽  
Input Output ◽  
Time Frequency ◽  
Time Varying Systems ◽  
System Representation

An analytical framework is developed that permits the input-output representations of discrete-time linear time-varying (LTV) systems in terms of biorthogonal bases on compact time intervals. Using these representations, the companion paper, Part II develops computational procedures for rapid identification of fast nonsmooth LTV systems based on short data records. One of the representations proposed is also used in H. Zhao and J. Bentsman, “Block Diagram Reduction of the Interconnected Linear Time-Varying Systems in the Time Frequency Domain,” accepted for publication by Multidimensional Systems and Signal Processing to form system interconnections, or wavelet networks, and develop subsystem connectibility conditions and reduction rules. Under the assumption that the inputs and the outputs of the plants considered in the present work belong to lp spaces, where p=2 or p=∞, their impulse responses are shown to belong to Banach spaces. Further on, by demonstrating that the set of all bounded-input bounded-output (BIBO) stable discrete-time LTV systems is a Banach space, the system representation problem is shown to be reducible to the linear approximation problem in the Banach space setting, with the approximation errors converging to zero as the number of terms in the representation increases. Three types of LTV system representation, based on the input-side, the output-side, and the input-output transformations, are developed and the suitability of each representation for matching a particular type of the LTV system behavior is indicated.

A Combined Time-Frequency Condition for Stability of Time-Varying Systems With One Nonlinearity

1971 ◽  
Vol 93 (4) ◽  
pp. 261-267 ◽  
Author(s):  
R. E. Blodgett ◽  
K. P. Young
Keyword(s):  
Stability Condition ◽  
Linear Time ◽  
Phase Variable ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Frequency Condition ◽  
Time Frequency ◽  
Time Varying Systems ◽  
The Stability ◽  
Limiting Case

A means is presented for determining stability of linear time-varying systems with one feedback nonlinearity. The stability condition involves the minimization of certain time functions of the system coefficients as well as the imaginary axis behavior of a polynomial. It is required that the equation of the linear time-varying system be asymptotically stable and be in phase variable form. The nonlinearity is restricted to lie in a sector. For the limiting case of an autonomous linear system the criterion reduces to the Popov stability condition in certain cases.

scholarly journals Instantaneous Modal Parameter Identification of Linear Time-Varying Systems Based on Chirplet Adaptive Decomposition

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Jie Zhang ◽  
Zhiyu Shi
Keyword(s):  
Parameter Identification ◽  
Energy Analysis ◽  
Linear Time ◽  
Damping Ratio ◽  
Energy Concentration ◽  
Time Varying ◽  
Modal Parameter ◽  
Modal Parameter Identification ◽  
Time Frequency ◽  
Time Varying Systems

Instantaneous modal parameter identification of time-varying dynamic systems is a useful but challenging task, especially in the identification of damping ratio. This paper presents a method for modal parameter identification of linear time-varying systems by combining adaptive time-frequency decomposition and signal energy analysis. In this framework, the adaptive linear chirplet transform is applied in time-frequency analysis of acceleration response for its higher energy concentration, and the response of each mode can be adaptively decomposed via an adaptive Kalman filter. Then, the damping ratio of the time-varying systems is identified based on energy analysis of component response signal. The proposed method can not only improve the accuracy of instantaneous frequency extraction but also ensure the antinoise ability in identifying the damping ratio. The efficiency of the method is first verified through a numerical simulation of a three-degree-of-freedom time-varying structure. Then, the method is demonstrated by comparing with the traditional wavelet and time-domain peak method. The identified results illustrate that the proposed method can obtain more accurate modal parameters in low signal-to-noise ratio (SNR) scenarios.

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