Discussion :

[x3-helene-87]

Bonjour !

Je vous présente mon très beau filtre H (numérique RIF) :
(figure 1 : abs(H), figure 2 : angle'H))



Il est donc en mémoire sous forme de coefficient.

Mon problème est que je voudrais garder juste la première bande passante, le reste le transformer en bande de réjection.
C'est à dire en faire un passe bas classique, de fréquence de coupure 40Hz.

quelqu'un sait quel outil je dois me servir ?

Merci d'avance !

[jyber]

Il faut choisir une méthode de synthèse, dont les plus classiques sont Butterworth (butter), Chebyshev (cheby1, cheby2), elliptique (ellip). Ces synthèses ne sont pas les seules, leur variété est illimitée. Ils ont chacun leur qualités et leur défaut, et la sélection doit se faire en fonction de la nature de l'application. Voila un petit showcase qui montre tout ce petit monde:

Code :

Sélectionner tout - Visualiser dans une fenêtre à part

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% Panoplie des IIR :
%		Butterworth
%		Chebyshev type 1
%		Chebyshev type 2
%		Elliptic (Cauer)
 
clear all; fig=1;
 
fs = 10000;		% Fréquence d_échantillonnage
fc =  1000;		% Fréquence de coupure
ripple = 3; 	% Ondulation (pour Chebyshev)
rejec = 40; 	% Réjection (pour Elliptic)
 
cutoff = fc/(fs/2);
bandep = [0.5*cutoff,2.0*cutoff];
 
%
% LOW-PASS
%
 
figure(fig++, 'name', 'low-pass filters');  clf;
 
subplot (2,2,1); grid on;
title ('Butterworth'); 
axis ([100,10000,-60,10]);
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
hold all; label = [];
for order = [2,4,6,8,10]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = butter(order,cutoff,'low');
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','northeast');
 
subplot (2,2,2); grid on;
title ('Chebyshev-1');
axis ([100,10000,-60,10]);
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
hold all; label = [];
for order = [2,4,6,8,10]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = cheby1(order,ripple,cutoff);
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','northeast');
 
subplot (2,2,3); grid on;
title ('Chebyshev-2');
axis ([100,10000,-60,10]);
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
hold all; label = [];
for order = [2,4,6,8,10]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = cheby2(order,rejec,cutoff);
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','northeast');
 
subplot (2,2,4); grid on;
title ('Elliptic');
axis ([100,10000,-60,10]);
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
hold all; label = [];
for order = [2,4,6,8,10]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = ellip(order,ripple,rejec,cutoff);
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','northeast');
 
 
%
% HIGH-PASS
%
 
figure(fig++, 'name', 'high-pass filters'); clf;
 
subplot (2,2,1); grid on;
title ('Butterworth');
axis ([100,10000,-60,10]);
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
hold all; label = [];
for order = [2,4,6,8,10]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = butter(order,cutoff,'high');
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','southeast');
 
subplot (2,2,2); grid on;
title ('Chebyshev-1');
axis ([100,10000,-60,10]);
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
hold all; label = [];
for order = [2,4,6,8,10]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = cheby1(order,ripple,cutoff,'high');
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','southeast');
 
subplot (2,2,3); grid on;
title ('Chebyshev-2');
axis ([100,10000,-60,10]);
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
hold all; label = [];
for order = [2,4,6,8,10]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = cheby2(order,rejec,cutoff,'high');
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','southeast');
 
subplot (2,2,4); grid on;
title ('Elliptic');
axis ([100,10000,-60,10]);
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
hold all; label = [];
for order = [2,4,6,8,10]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = ellip(order,ripple,rejec,cutoff,'high');
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','southeast');
 
%
% PASSBAND
%
 
figure(fig++, 'name', 'band-pass filters'); clf;
 
subplot (2,2,1); grid on;
title ('Butterworth');
axis ([100,10000,-60,10]);
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
hold all; label = [];
for order = [2,4,6]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = butter(order,bandep);
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','northeast');
 
subplot (2,2,2); grid on;
title ('Chebyshev-1');
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
axis ([100,10000,-60,10]);
hold all; label = [];
for order = [2,4,6]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = cheby1(order,ripple,bandep);
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','northeast');
 
subplot (2,2,3); grid on;
title ('Chebyshev-2');
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
axis ([100,10000,-60,10]);
hold all; label = [];
for order = [2,4,6]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = cheby2(order,rejec,bandep);
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','northeast');
 
subplot (2,2,4); grid on;
title ('Elliptic');
axis ([100,10000,-60,10]);
xlabel ('Frequence (Hz)');
ylabel ('Attenuation (dB)');
hold all; label = [];
for order = [2,4,6]
	label = [label ; sprintf("n=%d",order)];
	[b,a] = ellip(order,ripple,rejec,bandep);
	[h,w] = freqz(b,a,10000,fs);
	semilogx(w,20*log10(abs(h)));
end
hold off; legend (cellstr(label),'location','northeast');
 
 
 
 
 
 
 
 
 
# http://octave.sourceforge.net/signal/overview.html
#
# In general, you should use the [z,p,k] syntax to design
# IIR filters. To analyze or implement your filter, you can
# then use the [z,p,k] output with zp2sos. If you design the 
# filter using the [b,a] syntax, you may encounter numerical 
# problems. These problems are due to round-off errors. They
# may occur for filter orders as low as 6. 
 
#	[z,p,k] = butter(order,cutoff,'low');
#	sos = zp2sos(z,p,k);