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bilinear.js
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/**
* Generic bilinear filter formula
*
* @module digital-filter/bilinear
*/
'use strict'
module.exports = function bilinear (data, param) {
let a = param.a
let b = param.b
let type = param.type
//type can be:band-pass, band-reject, high-pass, high-reject
y[i] = a0 * x[i] + a1 * x[i-1] - b1 * y[i-1] - b2 * y[i-2]
}
let order = {
1: () => {
let A, A0, A1, B0, B1, a0, a1, b1
let A1C = A1*C, B1C = B1*C
A = B0 + B1C
a0 = (A0 + A1C) / A
a1 = (A0 - A1C) / A
b1 = (B0 - B1C) / A
},
2: () => {
let A, B0, B1, B2, A0, A1, A2, a0, a1, a2, b1, b2
let C2 = C*C
let A1C = A1*C, A2C = A2*C2
let B1C = B1*C, B2C = B2*C2
A = B0 + B1C + B2C
a0 = ( A0 + A1*C + A2*C2) / A
a1 = (2*A0 - 2*A2*C2) / A
a2 = ( A0 - A1*C + A2*C2) / A
b1 = (2*B0 - 2*B2*C2) / A
b2 = ( B0 - B1*C + B2*C2) / A
}
3: () => {
let A, B0, B1, B2, B3, A0, A1, A2, A3, a0, a1, a2, a3, b1, b2, b3
let C2 = C*C, C3 = C*C*C
let A1C = A1*C, A2C = A2*C2, A3C = A3*C3
let B1C = B1*C, B2C = B2*C2, B3C = B3*C3
A = B0 + B1C + B2C + B3C
a0 = ( A0 + A1C + A2C + A3C) / A
a1 = (3*A0 + A1C - A2C - 3*A3C) / A
a2 = (3*A0 - A1C - A2C + 3*A3C) / A
a3 = ( A0 - A1C + A2C - A3C) / A
b1 = (3*B0 + B1C - B2C - 3*B3C) / A
b2 = (3*B0 - B1C - B2C + 3*B3C) / A
b3 = ( B0 - B1C + B2C - B3C) / A
},
4: () => {
let A, B0, B1, B2, B3, B4, A0, A1, A2, A3, A4, a0, a1, a2, a3, a4, b1, b2, b3, b4
let C2 = C*C, C3 = C*C*C, C4 = C2*C2
let A1C = A1*C, A2C = A2*C2, A3C = A3*C3, A4C = A4*C4
let B1C = B1*C, B2C = B2*C2, B3C = B3*C3, B4C = B4*C4
A = B0 + B1C + B2C + B3C + B4C
a0 = ( A0 + A1C + A2C + A3C + A4C) / A
a1 = (4*A0 + 2*A1C - 2*A3C - 4*A4C) / A
a2 = (6*A0 - 2*A2C + 6*A4C) / A
a3 = (4*A0 - 2*A1C + 2*A3C - 4*A4C) / A
a4 = ( A0 - A1C + A2C - A3C + A4C) / A
b1 = (4*B0 + 2*B1C + - 2*B3C - 4*B4C) / A
b2 = (6*B0 - 2*B2C + 6*B4C) / A
b3 = (4*B0 - 2*B1C + 2*B3C - 4*B4C) / A
b4 = ( B0 - B1C + B2C - B3C + B4C) / A
},
5: () => {
let A, B0, B1, B2, B3, B4, B5, A0, A1, A2, A3, A4, A5, a0, a1, a2, a3, a4, a5, b1, b2, b3, b4, b5
let C2 = C*C, C3 = C*C*C, C4 = C2*C2, C5 = C2*C3
let A1C = A1*C, A2C = A2*C2, A3C = A3*C3, A4C = A4*C4, A5C = A5*C5
let B1C = B1*C, B2C = B2*C2, B3C = B3*C3, B4C = B4*C4, B5C = B5*C5
A = B0 + B1C + B2C + B3C + B4C + B5C
a0 = ( 1*A0 + 1*A1C + 1*A2C + 1*A3C + 1*A4C + 1*A5C) / A
a1 = ( 5*A0 + 3*A1C + 1*A2C - 1*A3C - 3*A4C - 5*A5C) / A
a2 = (10*A0 + 2*A1C - 2*A2C - 2*A3C + 2*A4C + 10*A5C) / A
a3 = (10*A0 - 2*A1C - 2*A2C + 2*A3C + 2*A4C - 10*A5C) / A
a4 = ( 5*A0 - 3*A1C + 1*A2C + 1*A3C - 3*A4C + 5*A5C) / A
a5 = ( 1*A0 - 1*A1C + 1*A2C - 1*A3C + 1*A4C - 1*A5C) / A
b1 = ( 5*B0 + 3*B1C + 1*B2C - 1*B3C - 3*B4C - 5*B5C) / A
b2 = (10*B0 + 2*B1C - 2*B2C - 2*B3C + 2*B4C + 10*B5C) / A
b3 = (10*B0 - 2*B1C - 2*B2C + 2*B3C + 2*B4C - 10*B5C) / A
b4 = ( 5*B0 - 3*B1C + 1*B2C + 1*B3C - 3*B4C + 5*B5C) / A
b5 = ( 1*B0 - 1*B1C + 1*B2C - 1*B3C + 1*B4C - 1*B5C) / A
},
6: () => {
let A, B0, B1, B2, B3, B4, B5, B6, A0, A1, A2, A3, A4, A5, A6, a0, a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6
let C2 = C*C, C3 = C*C*C, C4 = C2*C2, C5 = C2*C3, C6 = C3*C3
let A1C = A1*C, A2C = A2*C2, A3C = A3*C3, A4C = A4*C4, A5C = A5*C5, A6C = A6*C6
let B1C = B1C, B2C = B2C, B3C = B3C, B4C = B4C, B5C = B5C, B6C = B6C
A = B0 + B1*C + B2*C2 + B4*C3 + B4*C4 + B5*C5 + B6*C6
a0 = ( A0 + A1C + A2C + A3C + A4C + A5C + A6C) / A
a1 = ( 6*A0 + 4*A1C + 2*A2C + - 2*A4C - 4*A5C - 6*A6C) / A
a2 = (14*A0 + 5*A1C - 2*A2C - 3*A3C - A4C + 5*A5C + 14*A6C) / A
a3 = (20*A0 - 4*A2C + 4*A4C - 20*A6C) / A
a4 = (15*A0 - 5*A1C - A2C + 3*A3C - A4C - 5*A5C + 15*A6C) / A
a5 = ( 6*A0 - 4*A1C + 2*A2C - 2*A4C + 4*A5C - 6*A6C) / A
a6 = ( A0 - A1C + A2C - A3C + A4C - A5C + A6C) / A
b1 = ( 6*B0 + 4*B1C + 2*B2C + - 2*B4C - 4*B5C - 6*B6C) / A
b2 = (14*B0 + 5*B1C - 2*B2C + 3*B3C - B4C + 5*B5C + 14*B6C) / A
b3 = (20*B0 + - 4*B2C + + 4*B4C - 20*B6C) / A
b4 = (15*B0 - 5*B1C - B2C + 3*B3C - B4C - 5*B5C + 15*B6C) / A
b5 = ( 6*B0 - 4*B1C + 2*B2C + - 2*B4C + 4*B5C - 6*B6C) / A
b6 = ( B0 - B1C + B2C - B3C + B4C - B5C + B6C) / A
}
}