Band limited signals that are sparse

1. How can you tell if a signal is band-limited?
2. Can a signal be band-limited and time limited?

How can you tell if a signal is band-limited?

A signal is said to be band-limited if the amplitude of its spectrum goes to zero for all frequencies beyond some threshold called the cutoff frequency.

Can a signal be band-limited and time limited?

Mathematically, a signal can never be truly band-limited. A law of Fourier transformations says that if a signal is finite in time, its spectrum extends to infinite frequency, and if its bandwidth is finite, its duration is infinite in time.