A sampling theorem with error estimation for S-transform

ABSTRACT

S-transform (ST) is an extension of wavelet transform (WT) and short-time Fourier transform (STFT). The ST is depended on a scalable and moving Gaussian window. It overcomes the low-resolution factor of STFT and tackles with a lack of phase in WT. The ST is a useful tool for signal processing and analysis. In this paper, the multiresolution analysis (MRA) related with ST is introduced and after that a sampling theorem associated with ST is proposed which is based on multiresolution subspace. Additionally, truncation and aliasing error generated due to the sampling process, are also derived. The theoretical determinations are exhibited and validated using simulation results.

KEYWORDS:

• S-transform
• multiresolution analysis
• time–frequency analysis
• sampling theorem
• sampling error

MSC:

• 42A38
• 62D05
• 62F40
• 65T92
• 65G30
• 65F35
• 97N50

Disclosure statement

No potential conflict of interest was reported by the authors.