MATLAB: How do i shorten this code

digital signal processinggraphplotting

Hi, i know this is a noob-grade question, but i've tried making a code for a low pass butterworth filter magnitude response. Only problem is that i can't seem to compress the code so that i can have multiple lines of factor N into the graph without repetitions.
omc=1;
om=[0:0.1:4];
x=om/omc;
N=1;
y=x.^(2*N);
z=(1+y).^(0.5);
H=1./z;
figure;plot (om,H,'b');
xlabel('frequency in radians/sec');ylabel('Magnitude');
title('Low Pass Butterworth magnitude response');
N=2;
y=x.^(2*N);
z=(1+y).^(0.5);
H=1./z;
hold on;plot(om,H,'r');hold off;
N=3;
y=x.^(2*N);
z=(1+y).^(0.5);
H=1./z;
hold on;plot(om,H,'g');hold off;
N=4;
y=x.^(2*N);
z=(1+y).^(0.5);
H=1./z;
hold on;plot(om,H,'k');hold off;
legend('N=1','N=2','N=3','N=4');

Best Answer

All you need to do is get om and N to be the same size. Meshgrid is great for this.
omc=1;
om=[0:0.1:4];
[N,om]=meshgrid(1:4,om);
x=om/omc;
y=x.^(2*N);
z=(1+y).^(0.5);
H=1./z;
plot(om,H)
legend('N=1','N=2','N=3','N=4');
xlabel('frequency in radians/sec');ylabel('Magnitude');
title('Low Pass Butterworth magnitude response');
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