id: 05651443
dt: j
an: 05651443
au: Liu, Yue-Lin; Kou, Kit-Ian; Ho, Io-Tong
ti: New sampling formulae for non-bandlimited signals associated with linear
    canonical transform and nonlinear Fourier atoms.
so: Signal Process. 90, No. 3, 933-945 (2010).
py: 2010
pu: Elsevier Science, Amsterdam
la: EN
cc: 
ut: sampling theorem; linear canonical transform; non-bandlimited signal;
    generalized sinc function; parameter $M$-Hilbert transform
ci: 
li: doi:10.1016/j.sigpro.2009.09.030
ab: Summary: The sampling theory is basic and crucial in engineering sciences.
    On the other hand, the linear canonical transform (LCT) is also of
    great power in optics, filter design, radar system analysis and pattern
    recognition, etc. The Fourier transform (FT), the fractional Fourier
    transform (FRFT), Fresnel transform (FRT) and scaling operations are
    considered as special cases of the LCT. In this paper, we structure
    certain types of non-bandlimited signals based on two ladder-shape
    filters designed in the LCT domain. Subsequently, these non-bandlimited
    signals are reconstructed from their samples together with the
    generalized sinc function, their parameter $M$-Hilbert transforms or
    their first derivatives and other information provided by the phase
    function of the nonlinear Fourier atom which is the boundary value of
    the Möbius transform, respectively. Simultaneously, mathematical
    characterizations for these non-bandlimited signals are given.
    Experimental results presented also offer a foundation for the sampling
    theorems established.
rv: