00 /**********************************************************************
01 Copyright (c) 2014 Mark C. Erickson
02
03 Permission is hereby granted, free of charge, to any person obtaining
04 a copy of this software and associated documentation files (the
05 "Software"), to deal in the Software without restriction, including
06 without limitation the rights to use, copy, modify, merge, publish,
07 distribute, sublicense, and/or sell copies of the Software, and to
08 permit persons to whom the Software is furnished to do so, subject to
09 the following conditions:
10
11 The above copyright notice and this permission notice shall be included
12 in all copies or substantial portions of the Software.
13
14 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
15 OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
16 MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
17 IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
18 CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
19 TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
20 SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
21 **********************************************************************/
22
Disclaimer...
23 desc:EQ, Low-Pass Nth-Order, v1.0.1
24 // slope = (M * -12 dB) / Octave
25
26 slider1:1000<20,16000,1>Cutoff [Hz]
27 slider2:2<2,12,2>Order [N]
28
29 @init
30 M = 1;
31
32 @slider
33
34 function find_D(index stages)
35 (
36 _k = index;
37 _M = stages;
38 2.0 * sin($pi*(2*_k-1)/(4*_M));
39 );
40
41 slider1 > 19 ? (
42 slider2 > 1 ? (
43 N = slider2; // order N, 2 < N < 12
44 M = N / 2; // # of cascaded elements M, 1 < M < 6
45 w = 2.0 * $pi * slider1 / srate;
46
47 d = find_D(1, M);
48 beta1 = 0.5 * (( 1.0 - d / 2.0 * sin(w) ) / ( 1.0 + d / 2.0 * sin(w) ));
49 gamma1 = ( 0.5 + beta1 ) * cos(w);
50 alpha1 = ( 0.5 + beta1 - gamma1 ) / 4.0;
51
52 M > 1 ? (
53 d = find_D(2, M);
54 beta2 = 0.5 * (( 1.0 - d / 2.0 * sin(w) ) / ( 1.0 + d / 2.0 * sin(w) ));
55 gamma2 = ( 0.5 + beta2 ) * cos(w);
56 alpha2 = ( 0.5 + beta2 - gamma2 ) / 4.0;
57 );
58
59 M > 2 ? (
60 d = find_D(3, M);
61 beta3 = 0.5 * (( 1.0 - d / 2.0 * sin(w) ) / ( 1.0 + d / 2.0 * sin(w) ));
62 gamma3 = ( 0.5 + beta3 ) * cos(w);
63 alpha3 = ( 0.5 + beta3 - gamma3 ) / 4.0;
64 );
65
66 M > 3 ? (
67 d = find_D(4, M);
68 beta4 = 0.5 * (( 1.0 - d / 2.0 * sin(w) ) / ( 1.0 + d / 2.0 * sin(w) ));
69 gamma4 = ( 0.5 + beta4 ) * cos(w);
70 alpha4 = ( 0.5 + beta4 - gamma4 ) / 4.0;
71 );
72
73 M > 4 ? (
74 d = find_D(5, M);
75 beta5 = 0.5 * (( 1.0 - d / 2.0 * sin(w) ) / ( 1.0 + d / 2.0 * sin(w) ));
76 gamma5 = ( 0.5 + beta5 ) * cos(w);
77 alpha5 = ( 0.5 + beta5 - gamma5 ) / 4.0;
78 );
79
80 M > 5 ? (
81 d = find_D(6, M);
82 beta6 = 0.5 * (( 1.0 - d / 2.0 * sin(w) ) / ( 1.0 + d / 2.0 * sin(w) ));
83 gamma6 = ( 0.5 + beta6 ) * cos(w);
84 alpha6 = ( 0.5 + beta6 - gamma6 ) / 4.0;
85 );
86
87 )
88 );
89
90 @sample
91 x_1 = spl0;
92 y_1 = 2.0 * ( alpha1 * ( x_1 + 2.0 * x1_1 + x2_1 ) + gamma1 * y1_1 - beta1 * y2_1 );
93 x2_1 = x1_1;
94 x1_1 = x_1;
95 y2_1 = y1_1;
96 y1_1 = y_1;
97 spl0 = y_1;
98
99 M > 1 ? (
100 x_2 = spl0;
101 y_2 = 2.0 * ( alpha2 * ( x_2 + 2.0 * x1_2 + x2_2 ) + gamma2 * y1_2 - beta2 * y2_2 );
102 x2_2 = x1_2;
103 x1_2 = x_2;
104 y2_2 = y1_2;
105 y1_2 = y_2;
106 spl0 = y_2;
107 );
108
109 M > 2 ? (
110 x_3 = spl0;
111 y_3 = 2.0 * ( alpha3 * ( x_3 + 2.0 * x1_3 + x2_3 ) + gamma3 * y1_3 - beta3 * y2_3 );
112 x2_3 = x1_3;
113 x1_3 = x_3;
114 y2_3 = y1_3;
115 y1_3 = y_3;
116 spl0 = y_3;
117 );
118
119 M > 3 ? (
120 x_4 = spl0;
121 y_4 = 2.0 * ( alpha4 * ( x_4 + 2.0 * x1_4 + x2_4 ) + gamma4 * y1_4 - beta4 * y2_4 );
122 x2_4 = x1_4;
123 x1_4 = x_4;
124 y2_4 = y1_4;
125 y1_4 = y_4;
126 spl0 = y_4;
127 );
128
129 M > 4 ? (
130 x_5 = spl0;
131 y_5 = 2.0 * ( alpha5 * ( x_5 + 2.0 * x1_5 + x2_5 ) + gamma5 * y1_5 - beta5 * y2_5 );
132 x2_5 = x1_5;
133 x1_5 = x_5;
134 y2_5 = y1_5;
135 y1_5 = y_5;
136 spl0 = y_5;
137 );
138
139 M > 5 ? (
140 x_6 = spl0;
141 y_6 = 2.0 * ( alpha6 * ( x_6 + 2.0 * x1_6 + x2_6 ) + gamma6 * y1_6 - beta6 * y2_6 );
142 x2_6 = x1_6;
143 x1_6 = x_6;
144 y2_6 = y1_6;
145 y1_6 = y_6;
146 spl0 = y_6;
147 );
148