Plotting multiple Magnitudes in one plot

Hello everyone,

I intend to use freqz() function I need to plot the magnitude for different border frequencies. But first I need to determine the cut off frequencies.

I used this code but which seems to not give me even a close response to this

%% INitializing Matlab Environment 
close all; 
clc;
clearvars;
%% 1.1
b=log10(8000);%stop frequency and 100Hz is the pass frequency
yc1=logspace(2,b,23);
yd=stem(yc1);
grid on
xlabel('Borders','FontSize',12);
ylabel('F (Hz)','FontSize',12);
set(gca,'YScale', 'log')


%%
m={};
n={};
h={};
ph={};
j={};
fs=21e3 %sampling frequency
for i= 1:1:23
    [u,o] = butter(1,[2*100/fs, (2*yc1(i))/fs],'bandpass');
    m{i}=u;
    n{i}=o;
    %freqz(m{i},n{i});
    [h{i},ph{i}]=freqz(m{i},n{i});
    figure
    subplot(2,1,1)
    hold on
    plot(ph{i},20*log10(abs(h{i})));
    
end 
hold off
grid
set(gca,'XLim',[0 1e4],'XTick',10.^(0:4),'YLim',[-12 0],'YTick',-12:2:0,'XScale', 'log')

Any Idea on what I am missing ?

Answer 1

[Star Strider]

Put the figure call before the loop, and remove the subplot call:

figure
hold on
for i= 1:1:23
    [u,o] = butter(1,[2*100/fs, (2*yc1(i))/fs],'bandpass');
    m{i}=u;
    n{i}=o;
    %freqz(m{i},n{i});
    [h{i},ph{i}]=freqz(m{i},n{i});
    plot(ph{i},20*log10(abs(h{i})));
end 
hold off

This does not exactly produce the plot you posted, however it will get you closer.

I leave the other details to you.

[Mehdi Jaiem]

Thank you it solves at least the multiplot issue !

[Star Strider]

As always, my pleasure!

Answer 2

[Mathieu NOE]

hello

according to the picture, your code needed a revision, see below

the bandwith of your filters (BW) should be proportionnal to the center frequency to have identical roll off curves when plotted in log axis

you can test with a fixed constant bandwith , it's no the right option

hope it helps !

%% INitializing Matlab Environment 
close all; 
clc;
clearvars;
%% 1.1
b=log10(8000);%stop frequency and 100Hz is the pass frequency
BW = 100; % fixed bandwith (Hz)
yc1=logspace(2,b,23);
yd=stem(yc1);
grid on
xlabel('Borders','FontSize',12);
ylabel('F (Hz)','FontSize',12);
set(gca,'YScale', 'log')
%%
fs=21e3 %sampling frequency

for i= 1:1:23
    BW = 100; % fixed bandwith (Hz) : NO !!!
    % BW should be proportionnal to center frequencies (not fixed)
    BW = yc1(i)/5;
    f_low = yc1(i) - BW/2;
    f_high = yc1(i) + BW/2;
    
    [B,A] = butter(1,[f_low, f_high]*2/fs,'bandpass');
    freq = logspace(log10(f_low/4),log10(f_high*4),100),
    [h]=freqz(B,A,freq,fs);
    figure(2)
    hold on
    semilogx(freq,20*log10(abs(h)));
    
end 
hold off
grid
set(gca,'XLim',[0 1e4],'XTick',10.^(0:4),'YLim',[-12 0],'YTick',-12:2:0,'XScale', 'log')

[Mehdi Jaiem]

Awesome thank you!

I have to review some notons then since I am new to this topic.

But there are two ine that I did not understand:

BW = yc1(i)/5; %why did you divide by 5
freq = logspace(log10(f_low/4),log10(f_high*4),100) % what is the perpose of 100?
semilogx(freq,20*log10(abs(h))); % I read about semilogx but I did not understand it. why not plot ?

[Mathieu NOE]

BW = yc1(i)/5; %why did you divide by 5

bandwith is a fraction of center frequency , the higher the division factor, the narrower the filter ; just adapt to your own needs

freq = logspace(log10(f_low/4),log10(f_high*4),100) % what is the perpose of 100?

this is the length we want for freq vector; try another value , like 10, and see the plot being not so smooth

semilogx(freq,20*log10(abs(h))); % I read about semilogx but I did not understand it. why not plot ?

try plot to see the difference