I am currently reading a section in the Handbook for MRI Pulse Sequence book where it says that the time-bandwidth product for a SINC pulse is given by:
$$ T \Delta f = Z $$
where $T$ is the length of the pulse, $\Delta f$ is the bandwidth and $Z$ is the number of zero crossings of the SINC pulse. Now, my question might be very naive but it says that this is a dimensionless quantity but I do not understand why that will be:
For example, if the bandwidth is described in radians/sec, does it not have units of radians? In that case, how does it relate to the number of zero crossings, which is indeed a discrete number.