# 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?

• They're talking about band-limited, not time-limited. This is about the spectrum of $g(t)$. – Matt L. Nov 5 '19 at 12:51
• Sure, i know that it's about the fourier spectrum, my problem is that g(w) (the transform of g(t)) it's always band limited, being it's fourier transform a simple translated sinc, which is always limited – Dario Formi Nov 5 '19 at 12:55
• Why is a sinc function in the frequency domain band-limited? – Matt L. Nov 5 '19 at 13:11
• I don't think the question can be answered without a proper definition of "can be considered band limited". What's that supposed to mean ? – Hilmar Nov 5 '19 at 13:19
• My answer would be $T=0$, which makes $g(t)=0$, which is bandlimited. – MBaz Nov 5 '19 at 16:07