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

Question

Vaban Dust 2018-3-14

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https://ww2.mathworks.cn/matlabcentral/answers/388344-how-can-i-implement-a-convolution-function-in-matlab-and-perform-it-on-the-following-signals-and-plo

评论： Walter Roberson 2021-12-29

采纳的回答： Abraham Boayue

在 MATLAB Online 中打开

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.

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Walter Roberson 2018-3-14

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

Vaban Dust 2018-3-15

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

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Answer 1

Abraham Boayue 2018-3-16

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https://ww2.mathworks.cn/matlabcentral/answers/388344-how-can-i-implement-a-convolution-function-in-matlab-and-perform-it-on-the-following-signals-and-plo#answer_310268

在 MATLAB Online 中打开

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);

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Niklas Endler 2020-10-20

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

Walter Roberson 2020-10-20

在 MATLAB Online 中打开

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

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Answer 2

Abhishek Ballaney 2018-3-15

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https://ww2.mathworks.cn/matlabcentral/answers/388344-how-can-i-implement-a-convolution-function-in-matlab-and-perform-it-on-the-following-signals-and-plo#answer_310128

编辑：Walter Roberson 2020-10-20

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

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Answer 3

Ankur Agrawal 2021-9-21

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https://ww2.mathworks.cn/matlabcentral/answers/388344-how-can-i-implement-a-convolution-function-in-matlab-and-perform-it-on-the-following-signals-and-plo#answer_791964

编辑：Walter Roberson 2021-12-29

在 MATLAB Online 中打开

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;