Representation and approximation of time-varying systems via real-valued discrete Gabor transforms

An efficient method for the representation and approximation of linear time-varying systems is presented, in this paper, via the fast real-valued discrete Gabor transform proposed in our previous work. The linear time-varying system is assumed to be given in the input-output or kernel representation (a kernel can actually be treated as a 2-D discrete-time signal in the form of a 2-D matrix like a 2-D image). The kernel representation has recently received attention because of the applicability in frozen-time analysis and design of optimal control for time-varying systems, but requires a large number of coefficients. Due to the capability of nonstationary signal compression, the Gabor transform is applied to transform the kernel into the joint time-frequency domain so that a compact representation of the system can be obtained through truncating the transform coefficients by using a thresholding strategy within a specified approximation error of the system. Compared with the existing method based on the traditional complex-valued discrete Gabor transform, the proposed method is faster and can more easily be implemented in software or hardware as well as leads to a more compact representation. Experimental results also demonstrated the efficiency of the proposed method.