Wave basis.m - Revision history

Kuprov: Update function See also links and function index membership

2026-06-06T18:43:06Z

Update function See also links and function index membership

Kuprov: Rename Arguments section heading to Parameters

2026-06-05T17:53:28Z

Rename Arguments section heading to Parameters

Kuprov: Normalise sequential blank lines

2026-04-25T11:31:44Z

Normalise sequential blank lines

Kuprov: Restore pre-bulk-edit wiki content

2026-04-05T14:50:57Z

Restore pre-bulk-edit wiki content

Kuprov: Sync syntax/arguments/outputs with current Spinach source

2026-04-05T14:04:57Z

Sync syntax/arguments/outputs with current Spinach source

Kuprov: /* Notes */

2019-07-24T13:45:18Z

‎Notes

Kuprov: /* Notes */

2019-07-24T13:45:05Z

‎Notes

Kuprov: /* Examples */

2019-07-24T13:44:29Z

‎Examples

Kuprov at 13:43, 24 July 2019

2019-07-24T13:43:53Z

Kuprov: Created page with "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_..."

2016-01-16T17:28:11Z

Created page with "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_..."

New page

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.

@@ Line 39: / Line 39: @@
 ==See also==
-[[sawtooth.m]], [[triwave.m]], [[shaped_pulse_af.m]], [[shaped_pulse_xy.m]], [[pulse_shape.m]]
+[[sawtooth.m]], [[triwave.m]], [[shaped_pulse_af.m]], [[shaped_pulse_xy.m]], [[pulse_shape.m]], [[bruker_write.m]], [[cartesian2polar.m]], [[chirp_pulse.m]], [[grad_pulse.m]], [[grad_sandw.m]], [[pmlg5.m]], [[polar2cartesian.m]], [[read_wave.m]], [[restrans.m]], [[rseq_compiler.m]], [[rsequence.m]], [[sech_pulse.m]], [[spinal.m]], [[vg_pulse.m]], [[Kernel_functions]]
 ''Version 2.4, authors: [[Ilya Kuprov]]''

@@ Line 6: / Line 6: @@
       basis_waves=wave_basis(basis_type,n_functions,n_steps)
-==Arguments==
+==Parameters==
         basis_type     - may be set to 'sine_waves', 'cosine_waves',

@@ Line 40: / Line 40: @@
 ==See also==
 [[sawtooth.m]], [[triwave.m]], [[shaped_pulse_af.m]], [[shaped_pulse_xy.m]], [[pulse_shape.m]]
 ''Version 2.4, authors: [[Ilya Kuprov]]''

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:wave_basis.m}} __NOTOC__
 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_func,n_points)
+     basis_waves=wave_basis(basis_type,n_functions,n_steps)
 ==Arguments==
-basis_type     - may be set to 'sine_waves', 'cosine_waves',
+       basis_type     - may be set to 'sine_waves', 'cosine_waves',
                          and 'legendre'. The sine and the cosine op-
                          tions return the corresponding functions in
@@ Line 15: / Line 14: @@
                          turns legendre polynomials in the [-1,1] in-
                          terval.
-−
-        n_func         - the number of functions to return (integer
+        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
+       basis_waves    - a matrix with the basis waves in columns
 ==Examples==
 First three Legendre polynomials, normalised to have a unit 2-norm:
@@ Line 45: / Line 36: @@
 ==Notes==
 Because the resulting waveforms are discretised, they are not precisely orthogonal under the standard scalar multiplication. An extra orthogonalisation 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]]''

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:wave_basis.m}} __NOTOC__
 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)
+basis_waves=wave_basis(basis_type,n_func,n_points)
 ==Arguments==
-       basis_type     - may be set to 'sine_waves', 'cosine_waves',
+basis_type     - may be set to 'sine_waves', 'cosine_waves',
                          and 'legendre'. The sine and the cosine op-
                          tions return the corresponding functions in
@@ Line 14: / Line 15: @@
                          turns legendre polynomials in the [-1,1] in-
                          terval.
-−
-        n_functions    - the number of functions to return (integer
+        n_func         - 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
+basis_waves    - a matrix with the basis waves in columns
 ==Examples==
 First three Legendre polynomials, normalised to have a unit 2-norm:
@@ Line 36: / Line 45: @@
 ==Notes==
 Because the resulting waveforms are discretised, they are not precisely orthogonal under the standard scalar multiplication. An extra orthogonalisation 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]]''

@@ Line 36: / Line 36: @@
 ==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.
+Because the resulting waveforms are discretised, 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==

← Older revision		Revision as of 13:44, 24 July 2019
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	[[File:legendres.png]]		[[File:legendres.png]]
−

	==Notes==		==Notes==