G.2  Definitionen der Filterfunktionen

G.2.1  Kritische Filter

> f := (P)->1/(1+P);

> an := n->(2^(1/n)-1)^(1/2);

> fn := (P,n)->(1+an(n) * P)^(-n);

G.2.2  Butterworth

> butterworth1 := (P)->fn(P,1);

> butterworth3 := P->1/((1+P) * (1+P+P^2));

> butterworth10 := P->1/((1+1.9754 * P+P^2) * (1+1.782 * P+P^2) * (1+1.4142 * P+P^2) * (1+0.9080 * P+P^ 2) * (1+0.3129 * P+P^2));

G.2.3  Bessel

> bessel1 := (P)->fn(P,1);

> bessel3 := P->1/((1+0.756 * P) * (1+0.996 * P+0.4772 * P^2));

> bessel10 := P->1/((1+1.0215 * P+0.2650 * P^2) * (1+0.9393 * P+0.2549 * P^2) * (1+0.7815 * P+0.2351 * P^2) * (1+0.5604 * P+0.2059 * P^2) * (1+0.2883 * P+0.1665 * P^2));

G.2.4  Tschebyscheff 1dB

> Tscheby1_1 := (P)->fn(P,1);

> Tscheby1_3 := P->1/((1+2.2156 * P) * (1+0.5442 * P+1.2057 * P^2));

> Tscheby1_10 := P->1/((1+6.3624 * P+22.7468 * P^2) * (1+1.1399 * P+4.5167 * P^2) * (1+0.3939 * P+1.9665 * P^2) * (1+0.1616 * P+1.2569 * P^2) * (1+0.0455 * P+1.0277 * P^2));

G.2.5  Tschebyscheff 3dB

> Tscheby3_1 := (P)->fn(P,1);

> Tscheby3_3 := P->1/((1+3.3496 * P) * (1+0.3559 * P+1.1923 * P^2));

> Tscheby3_10 := P->1/((1+5.4449 * P+31.3788 * P^2) * (1+0.7414 * P+4.7363 * P^2) * (1+0.2479 * P+1.9952 * P^2) * (1+0.1008 * P+1.2638 * P^2) * (1+0.0283 * P+1.0304 * P^2));

G.2.6  Allpass

> Allpass_1 := P-> (1-0.6436 * P)/(1+0.6436 * P);

> Allpass_3 := P -> ((1-1.1415 * P) * (1-1.5092 * P+1.0877 * P^2))/((1+1.1415 * P) * (1+1.5092 * P+1.087 7 * P^2));

> Allpass_10 := P->( (1-2.8406 * P+2.0490 * P^2) * (1-2.6120 * P+1.9714 * P^2) * (1-2.1733 * P+1.8184 * P^2) * (1-1.5583 * P+1.5923 * P^2) * (1-0.8018 * P+1.2877 * P^2) )/ ( (1+2.8406 * P+2.0490 * P^2) * (1+2.6120 * P+1.9714 * P^2) * (1+2.1733 * P+1.8184 * P^2) * (1+1.5583 * P+1.5923 * P^2) * (1+0.8018 * P+1.2877 * P^2) ) ;

G.2.7  Schwingkreis

> Schwink := (P,Q) -> (1+P * Q) / (1+P/Q+P^2);

> simplify(evalc(Re(Schwink(I * Omega,Q))));

> simplify(evalc(Im(Schwink(I * Omega,Q))));