Sinc methods for quadrature and differential equations
Sinc methods for quadrature and differential equations
Time-frequency analysis: theory and applications
Time-frequency analysis: theory and applications
New sampling formulae for the fractional Fourier transform
Signal Processing
Sampling of linear canonical transformed signals
Signal Processing
New sampling formulae related to linear canonical transform
Signal Processing
A sampling theorem for non-bandlimited signals using generalized Sinc functions
Computers & Mathematics with Applications
Eigenfunctions of linear canonical transform
IEEE Transactions on Signal Processing
A sampling expansion for nonbandlimited signals in chromatic derivatives
IEEE Transactions on Signal Processing
The fractional Fourier transform and time-frequency representations
IEEE Transactions on Signal Processing
Sampling signals with finite rate of innovation
IEEE Transactions on Signal Processing
Windowed linear canonical transform and its applications
Signal Processing
Multi-channel filter banks associated with linear canonical transform
Signal Processing
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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 Mobius transform, respectively. Simultaneously, mathematical characterizations for these non-bandlimited signals are given. Experimental results presented also offer a foundation for the sampling theorems established.