wirtz
/
music-synthesizer-for-android
mirror of https://github.com/dcoredump/music-synthesizer-for-android.git
1
0
Fork 0
Code Issues Releases Wiki Activity

Fix little bugs in notebook

Browse Source 
Apparently nbviewer needs $$ to render math mode correctly? Hopefully
this will work.
master
Raph Levien 11 years ago
parent 1a614821f5
commit 4465659857
1 changed files with 6 additions and 4 deletions
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Show Stats Download Patch File Download Diff File
  1. 10
      lab/Second order sections in matrix form.ipynb

10
lab/Second order sections in matrix form.ipynb
Unescape View File

@ -42,16 +42,18 @@
"the output, and a scalar for the zero-delay contribution of the input to the output. For mathematical convenience, we group\n", "the output, and a scalar for the zero-delay contribution of the input to the output. For mathematical convenience, we group\n",
"the last two into a single 3-vector. Thus, a filter is described as the tuple $(\\mathbf{A}, B, C)$, and each step is as follows:\n", "the last two into a single 3-vector. Thus, a filter is described as the tuple $(\\mathbf{A}, B, C)$, and each step is as follows:\n",
"\n", "\n",
"$$\n",
"\\begin{align}\n", "\\begin{align}\n",
" out_n & = C \\cdot concat([[x_n], y_n]) \\\\\n", " out_n & = C \\cdot concat([[x_n], y_n]) \\\\\n",
" y_{n+1} & = B \\cdot x_n + \\mathbf{A} \\cdot y_n\n", " y_{n+1} & = B \\cdot x_n + \\mathbf{A} \\cdot y_n \\\\\n",
"\\end{align}\n", "\\end{align}\n",
"$$\n",
"\n", "\n",
"Where the $\\cdot$ notation represents dot product, vector times scalar, or matrix times vector multiplication, respectively.\n", "Where the $\\cdot$ notation represents dot product, vector times scalar, or matrix times vector multiplication, respectively.\n",
"\n", "\n",
"Question: would it be more convenient to have a single 3x3 matrix?\n", "Question: would it be more convenient to have a single 3x3 matrix?\n",
"\n", "\n",
"There is some redundancy in this representation. Obviously, multiplying A and B times some scalar, and dividing C by the same,\n", "There is some redundancy in this representation. Obviously, multiplying B times some scalar, and dividing C by the same,\n",
"is a filter with the same results. More subtly, the y vector can be transformed by any non-degenerate linear transformation.\n", "is a filter with the same results. More subtly, the y vector can be transformed by any non-degenerate linear transformation.\n",
"However, these transforms do matter when the filter parameters are modulated, which is especially common in synthesizers, and\n", "However, these transforms do matter when the filter parameters are modulated, which is especially common in synthesizers, and\n",
"also matter for roundoff behavior (particularly important when evaluating the filters using 32 bit floating point arithmetic).\n", "also matter for roundoff behavior (particularly important when evaluating the filters using 32 bit floating point arithmetic).\n",
@ -85,7 +87,7 @@
"y vector represents the two state variables in transposed direct form II. For review, the transfer function of this\n", "y vector represents the two state variables in transposed direct form II. For review, the transfer function of this\n",
"filter is:\n", "filter is:\n",
"\n", "\n",
"\\begin{equation} H(z) = \\frac{b_0 + b_1 z^{-1} + b_2 z^{-2}}{1 + a_1 z^{-1} + a_2 z^{-2}} \\end{equation}" "$$ H(z) = \\frac{b_0 + b_1 z^{-1} + b_2 z^{-2}}{1 + a_1 z^{-1} + a_2 z^{-2}} $$"
] ]
}, },
{ {
@ -208,7 +210,7 @@
"source": [ "source": [
"Simper prefers a resonance control that ranges from 0 to 1. If you prefer the classic Q, just use this conversion:\n", "Simper prefers a resonance control that ranges from 0 to 1. If you prefer the classic Q, just use this conversion:\n",
"\n", "\n",
"\\begin{equation} res = 1 - .5/Q \\end{equation}\n", "$$ res = 1 - .5/Q $$\n",
"\n", "\n",
"Let's test the filter out:" "Let's test the filter out:"
] ]

Write Preview
Loading…
Cancel
Save