# Wave basis.m

From Spinach Documentation Wiki

Common basis sets for the expansion of pulse waveforms. Returns the wave- form basis functions as columns of a matrix. Syntax:

basis_waves=wave_basis(basis_type,n_functions,n_steps)

Parameters:

basis_type - may be set to 'sine_waves', 'cosine_waves', and 'legendre'. The sine and the cosine op- tions return the corresponding functions in the [-pi,pi] interval, legendre option re- turns legendre polynomials in the [-1,1] in- terval.

n_functions - the number of functions to return (integer frequencies starting from zero on the case of cosines, integer frequencies starting from 1 inthe case of sines, legendre poly- nomial ranks in the case of legendre func- tion basis set.

n_points - number of discretization points.

Note: Because the resulting waveforms are discretized, they are not precisely orthogonal under the standard scalar multiplication. An extra orthogonalization step is therefore applied to make them orthogonal as vectors.