4f217321-7357-4b2f-9587-3de5a33fdeb3 188 4 5 false false false 0 0 decimal
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]

Решение системы нел.уравнений демпфированным методом Ньютона-Рафсона-Канторовича

x0 N ε #v1 #F #v2 #J f_nrk x x0 : its 1 100 range J x #J eval : f x #F eval : L f norme : 1 3 mat x1 J J x * f - eval dn_LinAlgLLS_SVD : Δx x1 x - : k 0 N 1 - ( range x1 x1 Δx k N / * - : x1 #F norme L < x x1 : break 2 1 line 0 if 2 1 line for 1 k N / - ( Δx * norme ε ≤ break 0 if 5 1 line for x eval 3 1 line :

--- Solves F(x)=0 for the system of non-linear equations ---

x.0 ns ε x f s f_nsolve n x f rows : j 1 n range k 1 n range J j k el x f j el x k el diff maple : for for x j J : sol x.0 ns ε x f x j f_nrk s x.0 ns ε x f x j al_nleqsolve cases : 4 1 line :

--- Solves F(x)=0 for the system of linear equations ---

x #f f_lsolve n x #f rows : v n 1 matrix #f : k 1 n range co n identity k col #f v - : j 1 n range L j k el co j el : for 2 1 line for L v - dn_LinAlgSolve 4 1 line :

Построение частотной х-ки цифровой пер функции, заданной a/b

a b ld npt zbode n a length : m b length : 1 2 mat f 0.5 10 0 npt 1 - ( range npt / 1 - ( ld * ^ vectorize * : z e 2 π * i * f * ( - ^ vectorize eval : 2 1 line k 1 npt range s a n el : u b m el : 1 2 mat n 2 ≥ j n 1 - ( 1 range s s z k el * a j el + eval : for 0 if m 2 ≥ j m 1 - ( 1 range u u z k el * b j el + eval : for 0 if r k el s u / eval : 4 1 line for θ 1 π / - ( r arg vectorize * eval : h 20 r abs vectorize 2 329 - ^ + log10 vectorize * eval : φ 2 Zeros : thr 1 2 52 - ^ - : 1 2 mat k 2 npt range φ 2 el θ k el θ k 1 - el - φ 1 el + : φ 2 el thr > φ φ 2 - : while φ 2 el thr - < φ φ 2 + : while θ k el θ k el φ 1 el + : 4 1 line for k npt : k 2 ≥ ( h k el h k 1 - el * 0 > ( & k k 1 - : continue for o θ k el 0 round eval : 0 npt 1 - ( range h θ o - ( 180 - ( * f augment eval 10 1 line :

Logarithmic X-scaling for Bode plots

ld loglin size 2048 : col green : X-axis p.1 ld - 0 + size col 1 5 mat : p.2 5 Zeros : 2 1 line 1 2 mat k 1 ld range n 2 10 range s col n 10 ≡ light col concat cases : v n 10 k ld 1 + ( - ^ * log10 0 + size s 1 5 mat : p.1 p.1 v stack : 3 1 line for x-labels d k ld 1 + ( - : s d 0 ≡ 1e d 0 < 1e+ cases d num2str concat cases : v d 0 s 8 brown 1 5 mat : p.2 v p.2 cols 1 ≡ p.2 v stack cases : 6 1 line for Y-axis y_margs 90 - 180 75 - range : p.3 5 Zeros : p.4 5 Zeros : 3 1 line 1 2 mat y y_margs v 0 y + size col 1 5 mat : p.3 v p.3 cols 1 ≡ p.3 v stack cases : v 0 y y num2str 8 brown 1 5 mat : p.4 v p.4 cols 1 ≡ p.4 v stack cases : 4 1 line for p.1 p.2 p.3 p.4 4 1 sys 7 1 line :

Decibel

x dB 20 x abs vectorize 2 329 - ^ + log10 vectorize * 1 1 line :

Bilinear Transform

A ω f_2z A ω f_iir2 f π ω * tan ( 1 - ^ : r 1 f 0 1 f - 0 0 0 0 3 3 mat A * A 3 2 el 0 ≡ 1 f f 2 ^ 2 0 2 f 2 ^ * - 1 0 f - f 2 ^ 3 3 mat A * cases : r r 1 2 el / eval 3 1 line : M 0 0 0 stack : k 1 A cols 2 / range M M A 1 A rows 2 k * 1 - 2 k * submatrix ω f_iir2 augment : for M 1 M rows 2 M cols submatrix eval 4 1 line :

Converts LPH->HPF in the S-domain

A f_2hp M 0 0 0 stack : k 1 A cols 2 / range u A 1 3 2 k * 1 - 2 k * submatrix : r u 3 3 range 1 2 range el 0 0 1 2 mat ≡ 0 0 1 1 0 0 0 1 0 3 3 mat u * u if reverse : M M r r 1 2 el / augment : 3 1 line for M 1 M rows 2 M cols submatrix eval 3 1 line :

Make the system of ORD equations for CIFB structure

equ k 1 ORD range eq k el k 1 > x k 1 - el b k 2 / el x k 1 + el * k 1 - 2 mod 0 cases - ( 1 if ( z k 2 mod ^ 1 z - / * x k el - : for eq 1 z - ( * vectorize 2 1 line :

Solve the equations symbolically and find numerator and denominator

H.z e1 ORD identity : x 1 ORD range el 0 : v equ 1 - ( * vectorize : find v 1 3 mat x e1 1 col : M equ v + : find M 1 3 mat k 2 ORD range x e1 k col : M M equ v + augment : 2 1 line for M M simplify maple : k 1 ORD range u M : j 1 ORD range u j k el v j el : for m k el u det a k el * : 3 1 line for nom m sum : k 0 ORD range n1 k 1 + el nom z k coeff simplify maple : d1 k 1 + el M det z k coeff simplify maple : 2 1 line for n1 d1 augment 9 1 line :

Get target NTF coefficients from EMQF filter

f.s 10 sqrt : f.z 0.01 : ntf.emqf A ORD f.s f_emqf f_2hp f.z f_2z : n1 1 : d1 1 : 1 2 mat k 1 A cols 2 / range n1 n1 A 2 k * 1 - col al_convr1d : d1 d1 A 2 k * col al_convr1d : 2 1 line for M n1 n1 1 el / d1 augment : k M rows 1 range d1 k el 0 ≠ break 0 if for 1 - ( ORD ^ M 1 k 1 M cols submatrix * eval 6 1 line : 3 1 sys

NTF for VMR modulator

ntf.emqf a b NH.z H.z : a 11.945664836945 10 3 - ^ * 152.1299971961772 10 6 - ^ * 900.1329807155925 10 9 - ^ * 2.843253341138510 10 9 - ^ * 3.748943391513047 10 12 - ^ * stack : b 4.183047168858502 10 6 - ^ * 919.4134984581749 10 9 - ^ * stack : L.z a b NH.z : L.z 2 col L.z 1 col L.z 2 col + augment 5 1 line : 1 - 4.999995 9.999985 - 9.999985 4.999995 - 1 1 - 4.987897 9.951747 - 9.927856 4.952061 - 0.988054 2 6 mat

Find CIFBR resonator coefficients b[n]

x1 x2 u nx t x.0 Clear nx ORD 2 / Floor : t u x1 x2 ntf 1 col 2 nx 1 + ( range el : u u ntf.emqf 1 col 2 nx 1 + ( range el - : 2 1 line : x2 f1 t simplify maple : x.0 4 10 5 - ^ * 1 10 5 - ^ * 1 10 6 - ^ * 10 6 - ^ stack 1 nx range el : sol_b x.0 its 11 : ε 2 52 - ^ : #x f1 nrk 0 : f_nsolve : 6 1 sys 8.809303796707 10 16 - ^ *

Find feed-foward coefficients a[n]

x u t Clear t u x sol_b ntf 2 col 2 ORD 1 + ( range el : u u ntf.emqf 2 col 2 ORD 1 + ( range el - : 2 1 line : x f2 t simplify maple : sol_a x f2 f_lsolve : 4 1 sys

Provide formal parameters with numerical values

1 a sol_a : b sol_b : h H.z eval : 3 1 sys a 2 u 34 26 20 14 9 5 1 stack - : ( ^ vectorize : b 2 v 15 16 18 stack - : ( ^ vectorize : h H.z eval : 3 1 sys if

Numerical values for VMR modulator

a 11.945664836945 10 3 - ^ * 152.1299971961772 10 6 - ^ * 900.1329807155925 10 9 - ^ * 2.843253341138510 10 9 - ^ * 3.748943391513047 10 12 - ^ * 5 1 mat : b 4.183047168858502 10 6 - ^ * 919.4134984581749 10 9 - ^ * 2 1 mat : 1 2 mat h H.z eval : 2 1 sys

Рисуем лог.диаграмму Боде для ампл. и фазы пер. фукции

Bp h 1 col h 2 col h 1 col 0 * + 4 500 zbode : 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plt 153.868 s *