Sampling of Signals Bandlimited to a Disc in the Linear Canonical Transform Domain

Abstract

We derive sampling formula for signals that are bandlimited to a disc of radius $R$ in the linear canonical transform (LCT) domain. By bandlimitedness in a disc $D$ in the LCT domain, we mean that the LCT $F(\omega)$ of a signal $f(t)$ vanishes outside the disc $D.$ We first express the signal in polar coordinates and then obtain the sampling formula. The samples of the angle $\theta$ are taken at $2N+1$ uniformly distributed points on the unit circle while the samples of the radial distance $r$ are taken at the zeros of the Bessel function. As a special case, we obtain sampling formula for signals that are bandlimited to a disc in the fractional Fourier transform domain.