Multichannel sampling expansions in the linear canonical transform domain associated with explicit system functions and finite samples

摘要

Focusing on two issues associated with the existing multichannel sampling expansions (MSEs) of the linear canonical transform (LCT), those are, the implicit expression of system functions possibly leads to the inconvenience of reconstructing signals in practical situations, and the reconstruction of the original signal from its finite samples, the authors first propose a novel MSE in the Fourier transform domain, providing an explicit expression for the response function of the reconstruction filter. Moreover on this basis, they formulate two kinds of LCT-type of MSEs related, respectively, to the modified convolution structure and the generalised convolution structure of the LCT. For these MSEs, though there is an explicit expression for system functions, the number of the signal's samples takes infinity. They then obtain multichannel interpolation formulae that interpolate a finite set of uniform samples through applying the derived MSEs to the LCT-band-limited, chirp periodic signals. They further present some possible applications of their proposals to show the advantage of the theory. Finally, the simulations are also performed to verify the correctness of the derived results.