# slowpass.m

Slow passage detection - calculates spectrum values at the user specified frequency positions using the Fourier transform of the Liouville - von Neumann equation. The biggest advantage over the fid+fft style detection is easy parallelization and the possibility of getting spectrum values at specific frequencies without recalculating the entire free induction decay.

## Syntax

    spectrum=slowpass(spin_system,parameters,H,R,K)


## Arguments

    parameters.sweep         vector with two elements giving
the spectrum frequency extents
in Hz

parameters.npoints       number of points in the spectrum

parameters.rho0          initial state

parameters.coil          detection state

H  - Hamiltonian matrix, received from context function

R  - relaxation superoperator, received from context function

K  - kinetics superoperator, received from context function


## Outputs

    spectrum  - the spectrum of the system with the specified
starting state detected on the specified coil
state within the frequency interval requested


## Examples

The 14N overtone MAS spectrum of glycine recorded using this method (examples/nmr_overtone/mas_glycine_1.m) appears below. FID+FFT simulation in this system is much slower.

## Notes

Relaxation must be present in the system dynamics, or the matrix inversion operation would fail to converge. The relaxation matrix R should *not* be thermalized.