On input-output relation of linear systems by use of PTI complex wavelet packet

This paper is concerned with an input output relation of linear systems when using the PTI (perfect translation invariance) complex wavelet packet transform. In general, the linear relation between input-output is guaranteed by the following two conditions: (I)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 PTI complex wavelet satisfying the above conditions has been used for demonstrating he linear relation. In this paper, a PTI complex wavelet packet transform is applied for improving the frequency resolution. The validity of our approach is shown through a numerical experiment.