How can I Implement a convolution function in MATLAB and perform it on the following signals and plot the results ?

Hi guys,

I have the following function:

impulse_response = zeros(1, length(input) + length(delta) - 1 );
for t_samp = 1:length(input)
for c_samp = 1:length(delta)
   index = t_samp + c_samp - 1;
value = delta(c_samp) * input(t_samp);
impulse_response(index) = impulse_response(index) + value;
end
end

I am new to Matlab and I want to understand how to Implement a convolution function in MATLAB and perform it on the following signals and plot the results ?

Task (1):

x[n] = [1,1,1,1] h[m] = [1,0,−1] x[n] = sin(n) h[m] = [−1,−2,8,−2,−1] 20 ≤ n < 20

Task (2): Given the input signal x[n]=0.3∗sin(n/5)+sin(n/50) : -Create your own delta signal h[m] that removes the higher frequency sinusoidal component to get yl[n].

Thanks in advance for your kind explanation.

[Walter Roberson]

Could you confirm that your n values are radians and not degrees?

[Vaban Dust]

Hi Walter, thanks for your quick reply. Actually our instructor didn't mention anything about n values type but let's presume they are radians not degrees

Answer 1

[Abraham Boayue]

Hey Vaban, you already got a code that implements convolution in matlab, all you need to do is to use it to solve your exercises: Alternatively, you could use matlab built in function called conv(), but it seems like your teacher wants you to learn how to code in matlab. Here is how you can use the code you have. Ex. Task 1.

% This is just a cleaner code, same as the one you posted
clear variables
close all
n = -20:20;
x = sin(n);            
h = [-1,-2,8,-2,-1];  
N = length(x);
M = length(h);
Ny = N + M -1;
y = zeros(1,Ny);
for i = 1:N
      for k = 1:M
       y(i+k-1) = y(i+k-1) + h(k)*x(i);
      end
end
m = 0: Ny-1;
% Make plot
figure
stem(m,y,'linewidth',3,'color','m')
grid;
a = title('Output of an LTI System y(n)');
set(a,'fontsize',14);
a = ylabel('y(n)');
set(a,'Fontsize',14);
a = xlabel('n');
set(a,'Fontsize',14);
% Using matlab built in function (you get the same results)
figure
y2 = conv(x,h);
stem(m,y2,'linewidth',3,'color','r')
grid;
a = title('Output y(n) using conv(x,h)');
set(a,'fontsize',14);
a = ylabel('y(n)');
set(a,'Fontsize',14);
a = xlabel('n ');
set(a,'Fontsize',14);

% % input = [1 1 1 1]; % input = x (n) = [1 1 1 1]
% % delta = [1 0 -1];  % h(m) = [-1 0 1]
% impulse_response = zeros(1, length(input) + length(delta) - 1 );
% for t_samp = 1:length(input)
% for c_samp = 1:length(delta)
%      index = t_samp + c_samp - 1;
%      value = delta(c_samp) * input(t_samp);
%      impulse_response(index) = impulse_response(index) + value;
% end
% end
% Ny = length(input) + length(delta)-1;
% y =  impulse_response;
% m = 0:Ny-1;
% % plot
% stem(m,y,'linewidth',3,'color','b')
% grid;
% a = title('Output of an LTI System y(n)');
% set(a,'fontsize',14);
% a = ylabel('y(n)');
% set(a,'Fontsize',14);
% a = xlabel('n [1 4]');
% set(a,'Fontsize',14);

[Vaban Dust]

Hi Abraham,

Thank you so much for your clear explanation. Now it is so clear for me how to us the convolution function. In the 2nd task, how should I know the high frequency ? and the h[m] should be corresponding to this freq ?

[Niklas Endler]

Correct me if I'm wrong but this only works in cases where the step function h[m] is symmetric?

[Walter Roberson]

discrete convolution and discrete filtering are the same mathematical operation, but they use the opposite convention on whether the matrix is applied left-to-right or right-to-left.

>> conv([1 2 3],[1 2 3])

ans =

     1     4    10    12     9

>> conv([1 2 3],fliplr([1 2 3]))

ans =

     3     8    14     8     3

conv() essentially flips the second vector and moves the result from left to right across the first vector; assume that there are zeros outside the first vector. This operation is thematically consistent with continuous convolution, as opposed to

Answer 2

[Abhishek Ballaney]

https://www.mathworks.com/help/matlab/ref/conv.html

Answer 3

[Ankur Agrawal]

n = -20:20;
x = sin(n);            
h = [-1,-2,8,-2,-1];  
N = length(x);
M = length(h);
Ny = N + M -1;
y = zeros(1,Ny);
for i = 1:N
    for k = 1:M
        y(i+k-1) = y(i+k-1) + h(k)*x(i);
    end
end
m = 0: Ny-1;

Answer 4

[Abdullah Mohmmed]

Write a MATLAB code to calculate and plot the two-sided convolution between the two discrete time signals x(n) and h(n) shown below

[Walter Roberson]

No signal definitions were shown.

And if they had been, we would have just referred you to the discussion above, which includes full code.