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In single carrier digital modulation methods, the resulting signal can be band limited by filtering to the first nulls and the signal can be demodulated and the data recovered with very little trouble. You can limit it to as much as half that bandwidth before it is theoretically impossible to demodulate and recover the data.
The flourier transform of the sinc function is just a rectangular window, that is, a ideal lowpass filter.
So, if what you said is a time domain signal, the bandwidth of it just the first zero point bandwidth, the same as the mainlobe.
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