Use output of a loop as its input to a filter

I am trying to build a cascade of filters so that the output of one is the input to the next one. The filters are all bandpass filters and I want to be able to have an input signal and have it run through all 32 bandpass filters in series. I also ultimately want to be able to specify a filter number to be able to look at the output after that specific filter number. This is what I have so far, I am having issues figuring out how to make the bottom loop apply the filter desgined in the top part of the code and how to make a loop which takes its own output and uses it as input. Thank you for your time! This is what I have:

close all
fs = 16e3;
numFilts = 32;
filter_number = 10;
%range = [50 8000];
CF1=linspace(50, 8000, 32) -50;
CF2=linspace(50, 8000, 32) +50;
for ii = 1:numel(CF1)-2
    bpfilt{ii} = designfilt( ...
        'bandpassfir', ...
        'FilterOrder',20, ...
        'CutoffFrequency1',CF1(ii+1), ...
        'CutoffFrequency2',CF2(ii+1), ...
        'SampleRate',fs);
    
    [h{ii},f] = freqz(bpfilt{ii}.Coefficients,1,4*8192,fs);
    
end
figure
subplot(211)
plot(f,db(abs([h{:}])));
title('Magnitude')
ylabel('Magnitude (dB)')
xlabel('Frequency (Hz)')
subplot(212);
plot(f,180/pi*(angle([h{:}])));
title('Phase')
ylabel('Phase (degrees)')
xlabel('Frequency (Hz)')
impulse_input = 0*fs;
impulse_input(1) = 1;

for ii = 1:numFilts-1
    [y,zf]=filter(impulse_input,:)
end

Answer 1

[Sulaymon Eshkabilov]

This is the code:

close all
fs = 16e3;
numFilts = 32;
filter_number = 10;
%range = [50 8000];
CF1=linspace(50, 8000, numFilts+2) -50;
CF2=linspace(50, 8000, numFilts+2) +50;
for ii = 1:numel(CF1)-2
    bpfilt{ii} = designfilt( ...
        'bandpassfir', ...
        'FilterOrder',20, ...
        'CutoffFrequency1',CF1(ii+1), ...
        'CutoffFrequency2',CF2(ii+1), ...
        'SampleRate',fs);
        [h{ii},f] = freqz(bpfilt{ii}.Coefficients,1,4*8192,fs);    
end
figure
subplot(211)
plot(f,db(abs([h{:}])));
title('Magnitude')
ylabel('Magnitude (dB)')
xlabel('Frequency (Hz)')
subplot(212);
plot(f,180/pi*(angle([h{:}])));
title('Phase')
ylabel('Phase (degrees)')
xlabel('Frequency (Hz)')

impulse_input = 0*fs;
impulse_input(1) = 1;
%%
% Reference signal with some white noise to benchmarch the created filter performances
t = linspace(0,2*pi,200);
rng(13)                                        % Make it repeatable
x = sin(t) + 0.25*rand(size(t));  % Ref Signal with a noise
% Simulation of 1-D digital filter:  x_filtered = filter(b, a, x); 
a = 1;    
figure
hold on

CoLoR = rand(numel(bpfilt), 3);
for ii = 1:numel(bpfilt)
  [x_filtered(ii,:),zf(:,ii)]=filter(bpfilt{1, ii}.Coefficients, a, x);
  plot(t,x_filtered(ii,:), 'LineWidth', 1.25, 'Color', CoLoR(ii,:))
  LEGs{ii} = ['Filter # ' num2str(ii)];
  legend(LEGs{:})
end
plot(t, x, 'k-', 'LineWidth', 2, 'DisplayName', 'Data')
xlabel('t')
ylabel('x(t) & x_{filtered} (t)')
grid on

legend('Show')
fprintf('Number of generated filters: %d \n', numel(bpfilt))

Number of generated filters: 32 

[S]

Thank you!

Answer 2

[Sulaymon Eshkabilov]

If understood your question correctly, this is what you are trying to simulate, e.g.:

close all
fs = 16e3;
numFilts = 32;
filter_number = 10;
CF1=linspace(50, 8000, 32) -50;
CF2=linspace(50, 8000, 32) +50;
for ii = 1:numel(CF1)-2
    bpfilt{ii} = designfilt( ...
        'bandpassfir', ...
        'FilterOrder',20, ...
        'CutoffFrequency1',CF1(ii+1), ...
        'CutoffFrequency2',CF2(ii+1), ...
        'SampleRate',fs);
    
    [h{ii},f] = freqz(bpfilt{ii}.Coefficients,1,4*8192,fs);
    
end
figure
subplot(211)
plot(f,db(abs([h{:}])));
title('Magnitude')
ylabel('Magnitude (dB)')
xlabel('Frequency (Hz)')
subplot(212);
plot(f,180/pi*(angle([h{:}])));
title('Phase')
ylabel('Phase (degrees)')
xlabel('Frequency (Hz)')

impulse_input = 0*fs;
impulse_input(1) = 1;
%%
% Create a reference signal with some white noise to benchmark the created filter performances
t = linspace(0,2*pi,200);
rng(13)                                        % Make it repeatable
x = sin(t) + 0.25*rand(size(t));               % Ref Signal with a noise
% Simulation of 1-D digital filter:  x_filtered = filter(b, a, x); 
a = 1;    
figure  % Visualize Filter performances:
hold on
CoLoR = rand(numel(bpfilt), 3);
for ii = 1:numel(bpfilt)
  [x_filtered(ii,:),zf(:,ii)]=filter(bpfilt{1, ii}.Coefficients, a, x);
  plot(t,x_filtered(ii,:), 'LineWidth', 1.25, 'Color', CoLoR(ii,:))
  LEGs{ii} = ['Filter # ' num2str(ii)];
  legend(LEGs{:})
end
plot(t, x, 'k-', 'LineWidth', 2, 'DisplayName', 'Data')
xlabel('t')
ylabel('x(t) & x_{filtered} (t)')
grid on

legend('Show')

[S]

So does this make the output of filter 1 be the input of filter 2? I am trying to go through and understand the loop but get a bit lost a the LEGs part

[S]

Also I was trying to use the impulse_input as the input to see if the impulse response looks correct but we can continue with the x you have too!

[S]

Just realized this too how come the number of filters went from 32 down to 30?

[Sulaymon Eshkabilov]

The variable LEGs is used to assign individual legend name for each set of filtered data plot to differentiate them. Since there are 30 sets of filter with outputs. So the answer is accepted and thumbs UP :) ?

All the best.

[S]

but there are 32 filters? also is the output of filter 1 being used as filter 2 input?

[Sulaymon Eshkabilov]

Here is the correct code to generate 32 filters.

close all
fs = 16e3;
numFilts = 32;
filter_number = 10;
%range = [50 8000];
CF1=linspace(50, 8000, numFilts+2) -50;
CF2=linspace(50, 8000, numFilts+2) +50;
for ii = 1:numel(CF1)-2
    bpfilt{ii} = designfilt( ...
        'bandpassfir', ...
        'FilterOrder',20, ...
        'CutoffFrequency1',CF1(ii+1), ...
        'CutoffFrequency2',CF2(ii+1), ...
        'SampleRate',fs);
        [h{ii},f] = freqz(bpfilt{ii}.Coefficients,1,4*8192,fs);    
end
figure
subplot(211)
plot(f,db(abs([h{:}])));
title('Magnitude')
ylabel('Magnitude (dB)')
xlabel('Frequency (Hz)')
subplot(212);
plot(f,180/pi*(angle([h{:}])));
title('Phase')
ylabel('Phase (degrees)')
xlabel('Frequency (Hz)')

impulse_input = 0*fs;
impulse_input(1) = 1;
%%
% Reference signal with some white noise to benchmarch the created filter performances
t = linspace(0,2*pi,200);
rng(13)                                        % Make it repeatable
x = sin(t) + 0.25*rand(size(t));  % Ref Signal with a noise
% Simulation of 1-D digital filter:  x_filtered = filter(b, a, x); 
a = 1;    
figure
hold on

CoLoR = rand(numel(bpfilt), 3);
for ii = 1:numel(bpfilt)
  [x_filtered(ii,:),zf(:,ii)]=filter(bpfilt{1, ii}.Coefficients, a, x);
  plot(t,x_filtered(ii,:), 'LineWidth', 1.25, 'Color', CoLoR(ii,:))
  LEGs{ii} = ['Filter # ' num2str(ii)];
  legend(LEGs{:})
end
plot(t, x, 'k-', 'LineWidth', 2, 'DisplayName', 'Data')
xlabel('t')
ylabel('x(t) & x_{filtered} (t)')
grid on

legend('Show')
fprintf('Number of generated filters: %d \n', numel(bpfilt))

Number of generated filters: 32 

[S]

Im getting: 'Number of generated filters: 30 '

[S]

Also just confirming this takes output of filter 1 as input to filter 2?

[Sulaymon Eshkabilov]

See the last code of mine with an output: Number of generated filters: 32 .

[S]

I did! I am still getting 30 for some reason. You only changes after impulse input right?

[Sulaymon Eshkabilov]

Just copy and paste my code above and it should give you 32 filters as shown above.

All the best.