Filterbank reconstruction of band‐limited signals from multichannel samples associated with the LCT

Abstract

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This study addresses the problem of filterbank implementation for multichannel sampling in the LCT domain. First, the interpolation and sampling identities in the LCT domain are derived by the properties of LCT. The interpolation identity is the key result of the current study, which establishes the equivalence of two signal processing operations. One of these uses continuous-timedomain filters, whereas the other uses discrete processing. Then, applying the interpolation identity, the particularly efficient filterbank implementation for derivative sampling, periodic non-uniform sampling and multichannel sampling are obtained in the LCT domain. Moreover, the authors present filterbank implementation using polyphase structures in LCT domain. Furthermore, the simulations are carried out to verify the effectiveness of the results and the potential applications of the multichannel sampling are also presented. Finally, combining the sampling and interpolation identity, they explore the relationship between the multichannel sampling and the filterbank in the LCT domain.

Uncertainty principles associated with the offset linear canonical transform

“…The two extra parameters, ie, time shifting τ and frequency modulation η , make the OLCT more general and flexible, and thereby the OLCT can apply to most electrical and optical signal systems. It basically says that the Fourier transform (FT), the fractional Fourier transform (FrFT), the Fresnel transform (FnT), the LCT, and many other widely used linear integral transforms in signal processing and optics are all special cases of the OLCT . Therefore, it is interesting to study the OLCT in a unified viewpoint of the above‐mentioned transforms.…”

“…It basically says that the Fourier transform (FT), the fractional Fourier transform (FrFT), the Fresnel transform (FnT), the LCT, and many other widely used linear integral transforms in signal processing and optics are all special cases of the OLCT. [12][13][14][15][16][17][18] Therefore, it is interesting to study the OLCT in a unified viewpoint of the above-mentioned transforms. Over the past few decades, there has been a vast amount of research on extending time-frequency analysis results that pertain to the FT or the LCT to the OLCT.…”

Cascaded interpolation‐filter‐delay‐decimation algorithm without additional delay

“…Most of these methods are based on approximation of fractional delay filter (e −jωD , D is the fractional delay) in frequency domain. However, by using sampling rate conversion method [11][12][13][14] based on Shannon's sampling theory and multirate signal processing method [15,16] based on Papoulis' generalised sampling expansion theory, the signal can be also delayed exactly with fractional delay [17,18], that is interpolation-filter-delay-decimation (IFDD) algorithm.…”