fix calculation of bandwidth of adiabatic hypsec pulse

[schuenke]

When trying to use a slice selective adiabatic hypsec pulse, I got several errors related to the calculation of the bandwidth of the hypsec pulse. I fixed the obvious ones like a wrong import of calc_rf_center() in calc_rf_bandwidth() and a wrong attribute name (rf.sig instead of rf.signal) and provide a new solution for the __find_flank() function:

    def __find_flank(x, f, c):
       m = np.max(np.abs(f))
       f = np.abs(f) / m
       i = np.argwhere(f > c)[0]

       return x[i]

Using calc_rf_bandwidth() with a cut_off value of 0.5 instead of 0.1 (which makes sense imo because the signal gets normalized to 1 and we are interested in the width at half maximum ?!) yields a bw of 1280 Hz, which is close to the literaure value of ~ 1250 Hz for the hypsec pulse with default settings (beta = 800, mu =4.9)

HOWEVER, simply using the analytic expression for the bw of a hypsec pulse makes far more sense imo. It is given by

bw = mu * beta / pi

As a reference, here the passage from Bernstein - Handbook of MRI pulse sequences:

Using the analytic expression is the way I implemented it now in make_adiabatic_pulse.py

[btasdelen]

@sravan953 I agree with @schuenke. I tested it, and it seems to give the correct bandwidth. It is much cleaner and less hand-wavy.