How to plot a smooth graph?

clc,clear all

b0 = 0.015;
b1 = 0.015;
b2 = 0.035;
b3 = 0.050;
v = 40; %velocity
L = 2;
w = (2*pi*v)/L; %angular frequency
F = w*(1/(2*pi)); %in Hz
t = linspace(0,10,18);

b = b0 + b1*sin(w*t) + b2*sin(2*w*t) 
+b3*sin(3*w*t);


plot(t,b)

Hi, I want to make this graph as being a smooth graph.

Thank you for your time.

[Rik]

Although you could resample your function to draw a smooth curve through your data points, that would not accurately describe your function. You can greatly increase the number of points in your t vector to see that you have an enormous amount of aliasing going on here. See this Wikipedia page for more information.

Answer 1

[Birdman]

You need to increase the step size of your t vector:

t = linspace(0,10,100);

Code:

b0 = 0.015;
b1 = 0.015;
b2 = 0.035;
b3 = 0.050;
v = 40; %velocity
L = 2;
w = (2*pi*v)/L; %angular frequency
F = w*(1/(2*pi)); %in Hz
t = linspace(0,10,100);
b = b0 + b1*sin(w*t)+b2*sin(2*w*t)+b3*sin(3*w*t);
plot(t,b)

[donghun lee]

Thank you for your help

[Rik]

if you increase the length of t to 2000 you will see that this will still be aliased. The code below is my attempt (mostly from memory) to apply the Nyquist criterion to determine the minimum number of samples you need for an actual smooth graph.

t_max=10;
n_samples=ceil(2*3*w*t_max);
t = linspace(0,t_max,n_samples);

If you set axis([0 1 -0.125 0.125]) you will be able to see the effect of the number of samples.

[donghun lee]

Hi Rik, I tried to simulate with the code you have attached, but it gives the length of t to 7540 and the graph gets really werid. Can you please explain this?

Thank you for your time.

[Rik]

That is why I suggested to zoom in. The weirdness is not from me, but actually from your function. If you want a true plot of your function you should increase the number of samples until further increasing it no longer changes your graph. For this function that starts at about 2500 samples. With about 10000 samples I no longer notice an improvement in smoothness.

You could avoid having to do this yourself by using fplot:

b0 = 0.015;
b1 = 0.015;
b2 = 0.035;
b3 = 0.050;
v = 40; %velocity
L = 2;
w = (2*pi*v)/L; %angular frequency
F = w*(1/(2*pi)); %in Hz
t_max=10;
b_fun =@(t) b0 + b1*sin(w*t)+b2*sin(2*w*t)+b3*sin(3*w*t);

fplot(b_fun,[0 t_max])
axis([0 1 -0.125 0.125])%zoom in to see detail

[donghun lee]

Ah!! Thank you soooo much for your help. I got what you mean now! I really appreciate it.

Thank you for your time again Rik!

Answer 2

[Walter Roberson]

t = linspace(0,10,18);

Increase the 18 to something larger, such as 50.

[donghun lee]

Thank you very much for your comment.