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I am trying to understand a MATLAB code of convolution animation.

Please check above link especially code in lines 15 and 16. I think author has mistakenly swapped comments of line 15 and 16. Please correct me if i am wrong

I am also placing the code here

close all
clear all
clc
% Initialization
t = -400:400; % Time range
X = zeros(1,length(t)); % Input signal 
x1 = -150; x2 = 150; % Range of Input Signal
H = zeros(1,length(t)); % Impulse Response
h1 = -50; h2 = 50; % Range of Impulse Response Signal
Y = zeros(1,length(t)); xh1 = x1+h1; xh2 = x2+h2; % Convolution output

% Input Signal Generation
x = sin(pi*t/10)./(pi*t/10); x(t==0)=1; % Generate Input Sinc Signal
h = t./t; h(t==0)=1; % Generate Impulse Response
H(t>=h1&t<=h2) = h(t>=h1&t<=h2); % Fit the input signal within range
X(t>=x1&t<=x2) = x(t>=x1&t<=x2); % Fit the impulse response within range

% Plot Input Signal and Impulse Response
subplot(3,2,1) 
plot(t,X,'b','LineWidth',3)
title('Input signal','FontWeight','b','FontSize',15)
grid on
subplot(3,2,2) 
plot(t,H,'r','LineWidth',3)
title('Impulse Response','FontWeight','b','FontSize',15)
grid on

for n = xh1:xh2 % Convolution limits
    % Convolution steps
    f = fliplr(X);           % Flip 
    Xm = circshift(f,[0,n]); % Shift
    m = Xm.*H;               % Multiply 
    Y(t==n) = sum(m);  % Sum
    
    % Live Convolution Process
    subplot(3,2,[3 4])
    plot(t,H,'r',t,circshift(fliplr(X),[0,n]),'b','LineWidth',3)
    title('Convolution Process: 1. Flip, 2. Shift, 3. Multiply 4.Sum','FontWeight','b','FontSize',15)
    grid on;
    % Result of convolution live
    subplot(3,2,[5 6]); 
    plot(t,Y,'k','LineWidth',3)
    axis tight
    grid on
    title('Convolution Output','FontWeight','b','FontSize',15)
    pause(0.01); % Pause between Update
    sgtitle('Illustration of 1D Convolution','FontWeight','b','FontSize',20)
    fig=gcf;
    fig.Units='normalized'; 
    fig.OuterPosition=[0 0 1 1]; %Open Current Figure in Maximized Mode
end

I have also attached a snap and highlighted relevant lines enter image description here

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  • $\begingroup$ Yes I agree with you; it appears the author has mistakenly swapped comments of line 15 and 16 $\endgroup$ Commented Mar 13, 2023 at 12:51

2 Answers 2

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Personally I found this code to be a little awkward but that's maybe just a matter of personal preference.

  1. Yes, the comments are swapped. Keep in mind though that convolution is commutative, i.e. $x*h = h*x$ and it doesn't matter which signal we call the impulse response or the input signal.
  2. h = t./t would be more readable as h = ones(size(t));
  3. Instead of copying the content, it feels more intuitive to explicitly set the non-signals areas to 0, i.e. H = h; H(t < h1 | t > h2) = 0;

Then again, that's just my personal preference.

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  • $\begingroup$ please explain your point(3). Do you meant to say that it can be replace Line 15 of code?? $\endgroup$
    – DSP_CS
    Commented Mar 13, 2023 at 14:03
  • $\begingroup$ yes. It replaces 14 and 15. $\endgroup$
    – Hilmar
    Commented Mar 13, 2023 at 14:35
  • $\begingroup$ you have written two command in your point (3). H = h; and H(t < h1 | t > h2) = 0; which of these two commands replaces line 15 of code?or they both need to be used? $\endgroup$
    – DSP_CS
    Commented Mar 13, 2023 at 14:41
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    $\begingroup$ Both are needed. Maybe you should consider basic Matlab class to get started? No offense, but that seems like a very basic question. $\endgroup$
    – Hilmar
    Commented Mar 13, 2023 at 14:46
  • $\begingroup$ h = t./t doesn’t work where h is 0. $\endgroup$ Commented Mar 15, 2023 at 21:23
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You may also see the Convolution Animation script from Matlab FileExchange. It has comments to make it easier to understand the process and flexibility to change the functions.

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