Two forms of a sampling theorem for concentric circles are established for a bandlimited two-dimensional (2-D) function. The location of the samples is prescribed either on equidistant circles or on the roots of the Bessel function J0( ). Both methods give comparable results, however, the number of samples required for their numerical evaluation is… (More)
N-th order Hankel Transforms are important for the reconstruction in Magnetic Resonance Imaging (MRI), CAT etc. In this contribution we derive new bounds on functions, which have bandlimited their n-th order Hankel Transform.
We develop the nth order Fourier-Bessel series expansion of 1-D functions in the interval (0,α). Hence we establish the sampling theorem for a function with α-bandlimited nth order Hankel Transform. The latter statement implies that the function is also Fourier Transform α-bandlimited. The samples' locations are given by the roots of nth order Bessel… (More)