A waveform is described as bandlimited if the frequency content of the signal is constrained to lie within a finite band of frequencies. This band is often described by an upper limit, the Nyquist frequency, assuming frequencies from DC up to his upper limit may be present. This concept can be extended to frequency bands that do not include DC.
A bandlimited signal cannot be also timelimited. More precisely, a function and its Fourier transform cannot both have finite support. This fact can be proved by using complex analysis and properties of Fourier transform.