I am looking for examples of signals that are band limited but also sparse. For instance, the spiking of the neurons can be modeled as banded in frequency domain and sparse in time domain. What other examples exists for such type of signals?
If a signal is sparse in the time domain, it has infinite support in the frequency domain, thus is not band-limited in the mathematical sense. However it might be so close to band-limited that the out-of-band spectrum disappears under the quantization or other noise floor.