modified the chebyshev12 routine to put out readily normalized circular harmonics and added

[mtx_circular_harmonics] to the file mtx_spherical_harmonics, as well as a corresponding helpfile.
why: useful for circular (1D) ambisonics, e.g. ...


svn path=/trunk/externals/iem/iemmatrix/; revision=11792

1 files changed, 186 insertions, 0 deletions

diff --git a/doc/mtx_circular_harmonics-help.pd b/doc/mtx_circular_harmonics-help.pd
new file mode 100644
index 0000000..2be06b0
--- /dev/null
+++ b/doc/mtx_circular_harmonics-help.pd
@@ -0,0 +1,186 @@
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+#X text 516 377 Franz Zotter \, 2009;
+#X text 129 226 for -n<=m<=n:;
+#X text 620 241 for m>=0;
+#X text 619 257 for m< 0;
+#X text 288 118 [mtx_circular_harmonics] requires a numerical creation
+argument <nmax> specifyiing the maximum order 0<=n<=nmax.;
+#X text 74 54 [mtx_circular_harmonics] circular harmonics evaluated
+at a set of points given in phi coordinates.;
+#X text 284 160 for an L points 2xL input matrix \, [mtx_spherical_harmonics]
+evaluates the (2*nmax+2) circular harmonics at L points and delivers
+an Lx(2*nmax+2) output matrix.;
+#X text 167 242 PHI_m(phi) = sqrt((2-delta_m) / (2*pi)) * cos(m*phi)
+;
+#X text 167 258 PHI_m(phi) = 1/sqrt(pi) * sin(m*phi);
+#X text 126 291 The order of the harmonics in the output columns is
+specified by the linear index k=nmax+m+1.;
+#X text 125 328 [mtx_circular_harmonics] uses fully normalized PHI_m.
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