[Show abstract][Hide abstract] ABSTRACT: Sampling is one of the fundamental topics in the signal processing community. Theorems proposed under this topic form the bridge between the continuous-time signals and discrete-time signals. Several sampling theorems, which aid in the reconstruction of signals in the linear canonical transform (LCT) domain, have been proposed in the literature. However, two main practical issues associated with the sampling of the LCT still remain unresolved. The first one relates to the reconstruction of the original signal from nonuniform samples and the other issue relates to the fact that only a finite number of samples are available practically. Focusing on these issues, this paper seeks to address the above from the LCT point of view. First, we extend several previously developed theorems for signals band-limited in the Fourier domain to signals band-limited in the LCT domain, followed by the derivation of the reconstruction formulas for finite uniform or recurrent nonuniform sampling points associated with the LCT. Simulation results and the potential applications of the theorem are also proposed.
Preview · Article · Dec 2008 · IEEE Transactions on Signal Processing
[Show abstract][Hide abstract] ABSTRACT: In this paper, a fractional Fourier transform (FRFT) based technique for the elimination of amplitude and phase distortions in the transmultiplexer (TMUX) is presented. The core elements of the TMUX, the synthesis and analysis filter banks cause amplitude and phase changes due to the filtering operations in the filter banks thereby altering the perfect reconstruction property. This study investigates a new approach to transmultiplexer design in the processing of the nonstationary signals.
[Show abstract][Hide abstract] ABSTRACT: The uniform sampling theorem and the reconstruction formulae associated with the fractional Fourier transform (FrFT) have been deduced in the literature, but the nonuniform sampling is yet to receive attention in the fractional Fourier domain. This paper focus on a special kind of non-uniform sampling process associated with the fractional Fourier transform. A nonuniform sampling model is first introduced and then, based on a useful lemma, the reconstruction formula for the nonuniform sampled signal points associated with the fractional Fourier transform is deduced. In addition, the classical results in the Fourier domain can be seen as a special case of our work.
[Show abstract][Hide abstract] ABSTRACT: Transmultiplexers, the basis of which is filter banks, have been successfully utilized for multiuser communications. One important limitation however, is the leakage of signal from one channel to another known as crosstalk. This occurs because the core elements, synthesis and analysis filters employed are nonideal. To minimize its effect has been the focus of transmultiplexer design. This study therefore investigates a new approach to transmultiplexer design using the FRFT based filter banks in the processing of nonstationary signals. This method can enhance the elimination of the crosstalk and amplitude distortion.