INPUT-OUTPUT RELATION OF LINEAR SYSTEMS BY USING COMPLEX WAVELET PACKET TRANSFORM

This paper is concerned with an input-output relation of linear systems when using the complex wavelet packet transform. In general, the linear relation between input-output is guaranteed by the following two conditions: (1) the mother wavelet has a better frequency resolution, and (2) the real and imaginary parts in the mother wavelet consist of a Hilbert transform pair. The complex wavelet satisfying the above conditions has been used for demonstrating the linear relation. In this paper, a complex wavelet packet transform is applied for improving the frequency resolution. The validity of our approach is shown through a numerical experiment.