Frequency-based window width optimization for [formula omitted]-transform

Abstract

The S -transform combines properties of the short-time Fourier (STFT) and wavelet transforms. It preserves the phase information of a signal as in the STFT, while providing the variable resolution as in the wavelet transform. However, the S -transform suffers from poor energy concentration for some classes of signals. A modification to the existing S -transform is proposed in this paper to enhance the energy concentration in the time–frequency domain. An improvement is achieved by introducing an additional parameter which can be used to optimize the window width. The optimization is performed over frequency and the proposed modification keeps the frequency marginal of the S -transform. The proposed scheme is tested on a set of synthetic signals. The results show that the proposed algorithm produces enhanced energy concentration in comparison to the standard S -transform. Also, the results show that for various signal types the proposed algorithm achieves higher signal concentration in comparison to other standard time–frequency transforms, such as, STFT and pseudo Wigner–Ville distribution (PWVD). Furthermore, it is concluded by numerical study that the proposed algorithm provides more accurate estimation of the instantaneous frequency than the standard S -transform.