How to create a periodic function?

The function at [0,2] is y=x for [0,1] and y=2-x for [1,2], I want the above function repeated at [2,10], so I need a periodic funtion in the whole [0,10], who can help me code it ,thank you.

Answer 1

[James Tursa]

Not sure what you mean by "repeated at [2,10]". Maybe this:

y = mod(x,2);
ix = y > 1;
y(ix) = 2 - y(ix);

[huazai2020]

Just like this

[James Tursa]

Plot what I gave you ...

[huazai2020]

Thank you, you give me the right code, but I cannot understand the code "y = mod(x,2);", could you please discribe it for me?

In addition, I want to use this one, could you help me revise it

[James Tursa]

Since you are making a periodic function, the mod(x,2) simply puts all of the input values into the range of one cycle. From there it is just a matter of forming the proper outputs of one cycle. The y=x part for the [0,1] input didn't need any adjustment so no extra code for that. Only the [1,2] part needed the extra code.

For this new function, you simply need to scale the x input properly and then use the same algorithm. E.g.,

y = mod(x/3,2);
ix = y > 1;
y(ix) = 2 - y(ix);

[huazai2020]

Thank you are right，but where can find the define of “mod”.

In addition, how can I revise the amplitude to 0.2, how can I revise it?

[James Tursa]

To revise the amplitude, simply add one more line to the algorithm:

y = 0.2 * y;

The mod( ) function description can be found here:

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

[huazai2020]

As I can see in the help document， mod has the function similar to division ，but not as you said. What is the reason?

mod

Modulus after division

Syntax

M = mod(X,Y)

Description

M = mod(X,Y) if Y ~= 0, returns X - n.*Y where n = floor(X./Y). If Y is not an integer and the quotient X./Y is within roundoff error of an integer, then n is that integer. The inputs X and Y must be real arrays of the same size, or real scalars.

The following are true by convention:

• mod(X,0) is X
• mod(X,X) is 0
• mod(X,Y) for X~=Y and Y~=0 has the same sign as Y.

[James Tursa]

Generic code could be:

% Periodic triangle wave
amplitude = whatever;
period = whatever;
y = mod(x,period);
ix = y > period/2;
y(ix) = period - y(ix);
y = (amplitude * 2 / period) * y;

[huazai2020]

Yes, you are so great,thank you so much.

Answer 2

[David Hill]

y=zeros(size(x));
for k=1:5
    y(x>=(k-1)*2&x<(k-1)*2+1)=x(x>=(k-1)*2&x<(k-1)*2+1);
    y(x>=2*(k-1)+1&x<2*k)=2-x(x>=2*(k-1)+1&x<2*k);
end

[huazai2020]

Hi， thank you for your answer，but I find it is not the results that I want as you see in the image，

clc;

clear all;

x=linspace(0,10,100);

y=zeros(size(x));

for k=1:5

y(x>=(k-1)*2&x<(k-1)*2+1)=x(x>=(k-1)*2&x<(k-1)*2+1);

y(x>=2*(k-1)+1&x<2*k)=2-x(x>=2*(k-1)+1&x<2*k);

end

plot(x,y)

[David Hill]

Are your functions changing? Recommend showing us the input and output you want.

[Image Analyst]

Then just use the code that you used to create the figure. It's what you want isn't it?

[huazai2020]

Please see the below image I upload，it is what I want.

Answer 3

[Setsuna Yuuki.]

You can use this function: https://es.mathworks.com/matlabcentral/fileexchange/83058-continuous-piecewise-function-linear-funcion-por-partes

x = [0:3:36];
y = [0 1 0 1 0 1 0 1 0 1 0 1 0];
sig = pwfun(x,y);

and create the waveform only with the intersection points.