  Sampling theory in fractional Fourier Transform (FrFT) domain has been
studied extensively in the last decades. This interest stems from the ability
of the FrFT to generalize the traditional Fourier Transform, broadening the
traditional concept of bandwidth and accommodating a wider range of functions
that may not be bandlimited in the Fourier sense. Beyond bandlimited functions,
sampling and recovery of sparse signals has also been studied in the FrFT
domain. Existing methods for sparse recovery typically operate in the transform
domain, capitalizing on the spectral features of spikes in the FrFT domain. Our
paper contributes two new theoretical advancements in this area. First, we
introduce a novel time-domain sparse recovery method that avoids the typical
bottlenecks of transform domain methods, such as spectral leakage. This method
is backed by a sparse sampling theorem applicable to arbitrary FrFT-bandlimited
kernels and is validated through a hardware experiment. Second, we present
Cram\'er-Rao Bounds for the sparse sampling problem, addressing a gap in
existing literature.
