How to Perform a Convolution in MATLAB | MATLAB Tutorial

Convolutions in MATLAB! How to take the convolution conv() of two functions f(t)*x(t) to generate a system response. Discrete functions and smoothing curves discussed with examples.

OVERVIEW
conv(a,b) is used to take the convolution of two functions. Be sure to scale your output! 3:06
If you want the output to have the same number of terms as 'a', use conv(a,b,'same').

CHAPTERS
0:00 Introduction
0:36 Part 1: Convolution of Two Functions f(t)*g(t)
1:57 Using conv()
2:25 Analyzing System Response
3:06 Scaling System Response
7:24 Part 2: Smoothing Curves
9:13 Using conv(a,b,'same')

MATH CORRECTIONS/COMMENTS on the video -- PLEASE READ!!
1. f(t)*g(t) is said "f convolved with g".
2. at 4:15 we see the max value of the output = max f(t) times max g(t) -- know that this does not always happen.
3. Scaling the t-axis / x-axis is not always straightforward. My scale and shift works in this case but doesn't apply to the general case.
4. at 5:50 you don't need the .* for (1:length(yt))*dt because this is a vector times a scalar.
5. at 6:50 take note I have only included the t2(1) term. However, for the general case, you may use t2(1) + t1(1) to account for your signals starting at different times. In this video, t1(1) was simply zero and thus adding only t2(1) worked.

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[mahdinemati]

your shift is wrong
the correct shift is : t1(1) + t2(1)
the resone is in Convolution we can swap => f(t)*x(t) = x(t)*f(t)
that's why we use : t1(1) + t2(1)
thank you for your great Tutorial

[ronlaspisa]

At exactly 2:26, your output of conv shows two unusual features - the value at t = 0 is not in the plot, and the max value of the result is 63 instead of 60. After you scale both output and t values, those details are gone, and your final results don't show those. However when I duplicate your code, I get a final graph that has the same two incorrect features. Do you have any idea why the graph at 2:26 is off? Maybe that would help me. Has 'conv' changed since your video? Thanks!

[burhanuddinsakarwala]

I could not understand what you had done from line 23 up till line 36, could you please show me what is going on there?

[jchopra]

Is there a specific formula you used for the Hamming curve?

[knightning]

here is working code for the first part.

clc, clearvars, close all
dt = 0.0001;

t1 = 0:dt:2;
ft = 2-t1;

t2 = -2:dt:2;
gt = 3*ones(1, length(t2));

yt = dt*conv(ft, gt);
yt_x = (1:length(yt)).*dt + t2(1) + t1(2);

figure(1)
subplot(2, 2, 1), plot(t1, ft, 'r'), title('f(t) impulse response'),
grid on, xlim([-2 2]), xlabel('t'), ylabel('amplitude')

subplot(2, 2, 3), plot(t2, gt, 'b'), title('g(t) system input'),
grid on, xlabel('t'), ylabel('amplitude'), ylim([0 3.5])

subplot(2, 2, [2;4]), plot(yt_x, yt, 'k'), title('f(t)*g(t) system response'),
grid on, xlabel('t'), ylabel('amplitude')