Chirp pulse.m

Chirp pulse waveform with a sine bell power or a quarter-sine amplitude fade-in and fade-out. Generates unidirectional chirps or saltire chirps which are super-positions of two counter-sweeping chirps.

Syntax

    [Cx,Cy,durs,ints,amps,phis,frqs]=chirp_pulse(npts,dur,bwidth,smp,type)

Arguments

       npts    - number of discretization points in
                 the waveform

   duration    - pulse duration, seconds

     bwidth    - chirp sweep bandwidth around
                 zero frequency, Hz

       type    - 'wurst', 'smoothed', or 'saltire'; the
                  default is uniform time grid, to get
                  adaptive sampling, add '-adaptive'

        smp    - smoothing parameter; for 'wurst', this
                 is the power in 
           
                              1-|sin(x)^smp|

                 as x approaches pi/2 at either the edge
                 of the pulse. For 'smoothed' and 'salti-
                 re', this is the fraction of the pulse
                 duration (in percent) that is affected
                 by a sine bell fade-in and fade-out: 0
                 means square amplitude envelope and 50
                 means sine bell envelope.

Outputs

         Cx    - real part of the waveform, calibrated to
                 produce an inversion pulse, rad/s

         Cy    - imag part of the waveform, calibrated to
                 produce an inversion pulse, rad/s

       durs    - slice durations for piecewise-constant
                 approximation, seconds

       ints    - interval durations for piecewise-linear
                 approximation, seconds

       amps    - waveform amplitudes, rad/s

       phis    - waveform phases, rad

       frqs    - waveform frequencies, Hz

  intv_grid    - normalised interval grid, npts-1 elements

Notes

Cy is zero for the saltire pulse, this radically changes its phase and amplitude profiles.

See also

Shaped pulses and gradients

Version 2.9, authors: Ilya Kuprov, Jean-Nicolas Dumez, Ludmilla Guduff, Maria-Grazia Concilio, Mohammadali Foroozandeh