An overall theoretical description of frequency slice wavelet transform

This paper presents an overall description of a new time–frequency signal analysis method, called frequency slice wavelet transform (FSWT). Five new properties of the FSWT are introduced as follows.

(1) The center of time–frequency window is the observing center in contrast to the wavelet transform (WT).

(2) FSWT can be controlled by the frequency resolution ratio of the measured signal.

(3) The original signal can be decomposed on a frequency slice function (FSF); theoretically, it can also be rebuilt by infinite correlation function (CF) with the FSF. At the same time, FSWT has many reconstructive procedures that are not directly related to the choice of the FSF. Furthermore, several useful transmutations for FSWT are proposed.

(4) The FSF can be designed very freely and can be ensured to have perfect symmetry in time and frequency domains.

(5) The FSWT has higher performance against noise than the WT.

Meanwhile, this paper reveals the theoretical comparisons with the WT method. Then some typical examples are used to demonstrate these facts.