When can a windowed cosine be considered band-limited signal? I have an exam in the following days and i have no clue of what is the response to this question in the exam:


  given this signal:
  
  $$g(t) = H\left(t+\frac{T}{3}\right) f(t) - H\left(t-\frac{2T}{3}\right)f(t)$$ $H(t)=$ Heaviside step function
  
  $f(t) = \cos(\omega_1 t)$
  
  Define a value of $T$ for which the signal $g(t)$ can be considered
  band limited.


This question doesn't make much sense to me. This is a windowed cosine function and it's bandwith depends on the value of $T$, it's always limited! 
Unless $T$ approches 0 and it can be seen as an impulse. Am I missing something?
T=0 or T=infinity.  

Any non-zero signal with finite length support in one domain has infinite support in the other domain.

cos(wt) is only theoretically band-limited if infinite in length.