How to make this code without using built-in convolution function.

clear all;
clc;
delta_t=0.0001;
t=[-6:delta_t:6];
x=(t>=-2)&(t<=2);
h=((t>=0)&(t<=3)).*((2/3)*t);
y=conv(x, h, 'same')*delta_t;
subplot(3,1,1); plot(t,x,'r'); grid on; ylim([-0.5 2]); ylabel('x(t)')    
subplot(3,1,2); plot(t,h,'m'); grid on; ylim([-0.5 3]); ylabel('h(t)') 
subplot(3,1,3); plot(t,y,'b'); grid on; ylim([-0.5 4]); ylabel('y(t)')

[Paul]

If you have a license for the Symbolic Math Toolbox, the closed-form expression for y can be obtained using syms, rectangularPulse, and int

Answer 1

[Manikanta Aditya]

To make the code without using the built-in convolution function, you can implement the convolution manually.

Check how you can do it:

clear all;
clc;

delta_t = 0.0001;
t = [-6:delta_t:6];
x = (t >= -2) & (t <= 2);
h = ((t >= 0) & (t <= 3)) .* ((2/3) * t);

% Manual Convolution
len_x = length(x);
len_h = length(h);
len_y = len_x + len_h - 1; % Length of the convolution output
y_manual = zeros(1, len_y); % Initialize the result array

% Perform the convolution operation manually
for i = 1:len_x
    for j = 1:len_h
        y_manual(i + j - 1) = y_manual(i + j - 1) + x(i) * h(j) * delta_t;
    end
end

% To match the 'same' size as the built-in conv function, we need to trim the result
% Calculate the start and end indices to trim y_manual to the same size as x
start_index = floor(len_h / 2);
end_index = start_index + len_x - 1;
y_manual_same_size = y_manual(start_index:end_index);

subplot(3,1,1); plot(t, x, 'r'); grid on; ylim([-0.5 2]); ylabel('x(t)')
subplot(3,1,2); plot(t, h, 'm'); grid on; ylim([-0.5 3]); ylabel('h(t)')
subplot(3,1,3); plot(t, y_manual_same_size, 'b'); grid on; ylim([-0.5 4]); ylabel('y(t)')

Thanks!

[Alexander]

Dear @Manikanta Aditya, just a suggestion: change "delta_t" to 0.01. Because the result is clear visible with 0.01 and an old beast (as my pc) takes minutes to finish. ;)

[Alexander]

Just forgotten, your contribution is very helpful to understand convolution. Thanks.

[Manikanta Aditya]

@Alexander, Thank you for the suggestation.

[Alexander]

Cheers.

[whyyss]

Thank you for your kindness. It was really helpful to me!!