How can I apply filter with loop-based function instaed of using filter( ) : built in MATLAB function?

Hello

I'm trying to plot the generated signal x against filtered x with loop-based function, but I don't know how to do it. Can somebody instuct me how to do it? Here is my attached code. Thank you for your help in advance!

%% Applying the filter to data

% create time sequence n for 501 samples from 0 to 500
n = linspace(0, 500, 500+1);

% assume a signal x 
x = 0.7*sin(0.02*pi*n) + sin(0.1*n)+ 0.1*sin(rand()*n);

plot(n,x)

%% Example : HPF

%{
Difference Equation 
 y[n] = 0.5x[n] + 0.4x[n-1] + 0.1x[n-2]
 in a form of [a]y = [b]x 
%}
a_1 = 1; b_1 = [0.5 0.4 0.1];

% apply filter
y_hpf1 = filter(b_1,a_1,x);

% plot the generated signal x against filtered x
figure();
plot(n,x);
title("x with HPF")
xlabel('\omega (rad)');
hold();
plot(n,y_hpf1);

Answer 1

[Jan]

You can find a Matlab function for filtering here: https://www.mathworks.com/matlabcentral/answers/9900-use-filter-constants-to-hard-code-filter#answer_13623 .

On the other hand: "y[n] = 0.5x[n] + 0.4x[n-1] + 0.1x[n-2]" is easy to implement and the question sounds like a homework assignement. Start with pre-allocating the output y, which has the same size as the input x:

y = zeros(size(x));

You cannot apply the formula to y(1), because there is no x(0) and x(-1). So use y(1) = 0.5 * x(1) and y(2) = 0.5 * x(2) + 0.4 * x(1). Then create a for loop to calculate the remaining elements.

[Krittanai]

I want the result to appear like this, but I can't.

Do you know where my code is wrong?

%% Applying the filter to data

% create time sequence n for 501 samples from 0 to 500
n = linspace(0, 500, 500+1);

% assume a signal x 
x = 0.7*sin(0.02*pi*n) + sin(0.1*n)+ 0.1*sin(rand()*n);

plot(n,x)

%% Example : HPF

%{
Difference Equation 
 y[n] = 0.5x[n] + 0.4x[n-1] + 0.1x[n-2]
 in a form of [a]y = [b]x 
%}
a = 2; b = [0.5 0.4 0.1];

% apply filter
y_hpf1 = myFilter(b,a,x);

% plot the generated signal x against filtered x
figure();
plot(n,x);
title("x with HPF")
xlabel('\omega (rad)');
hold();
plot(n,y_hpf1);

function [y, z] = myFilter(b, a, x, z)
n    = length(a);
z(n) = 0;

b = b / a(1);
a = a / a(1);

y = zeros(size(x));
for m = 1:length(y)
    y(m) = b(1) * x(m) + z(1);
    for i = 2:n
        z(i -1) = b(i)*x(m)+z(i)-a(i)*y(m);
    end
end
z = z(1:n - 1);
end

[Krittanai]

Also, I have to use "y[n] = 0.5x[n] + 0.4x[n-1] + 0.1x[n-2]" & "y[n] = 0.5x[n] - 0.4x[n-1] - 0.1x[n-2]" as the problem states.

[Jan]

@Krittanai: "but I can't" - please mention, what this means. It is easier to solve a problem than to guess, what the problem is. So if you get an error message, read it and if you do not understand it, post a copy of the complete copy here. If the result differ from your expectations, explain the difference.

The simple method myFilter assumes, that the filter parameters a and b have the correct dimensions:

a = [2, 0, 0];      % Not just a = [2]
b = [0.5 0.4 0.1];

You find a version on the linked page, which cares for scalar a also (Link)

"I have to use "y[n] = 0.5x[n] + 0.4x[n-1] + 0.1x[n-2]" " - then simply convert this to Matlab:

for k = 3:length(x)
    y(k) = 0.5 * x(k) + 0.4 * x(k-1) + 0.1 * x(k-2);
end

I've inserted * for the multiplication and converted [ and ] to ( and ). You see, this is not magic.

I've mentioned before, that the first 2 elements of y need extra care.