wave_basis.m

Common basis sets for the expansion of pulse waveforms. Returns the waveform basis functions as columns of a matrix.

Syntax

    basis_waves=wave_basis(basis_type,n_functions,n_steps)

Arguments

      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.

Outputs

      basis_waves    - a matrix with the basis waves in columns

Examples

First three Legendre polynomials, normalised to have a unit 2-norm:

    a=wave_basis('legendre',3,200); plot(a);

Notes

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. As a result, some functions may be upside-down.

See also

sawtooth.m, triwave.m, shaped_pulse_af.m, shaped_pulse_xy.m, pulse_shape.m

Version 2.4, authors: Ilya Kuprov